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Programme & Abstracts
SANUM 2011
The 35th AnnualSouth African Symposium on
Numerical and Applied Mathematics
23, 24 and 25 March
Hosted by theDepartment of Mathematical Sciences
Stellenbosch UniversitySouth Africa
Welcome to SANUM!
Registration takes place on Wednesday 23 March from 08:15 to 08:50 in the foyer of the Van der Sterr (mathematics) building, located behind the Neelsie student centre between Victoria and Merriman roads.
On the cover: Panoramic view of Stellenbosch from Papegaaiberg. Photo by Francois Malan.
Internet Access, Reception, Lunches
Internet access is available on four computers in room 3013 (third floor).
To enable internet access, run the NXInetkey program from the desktop.
Login: twbesoekersPassword: Sanumconf11
We are charged per megabyte, so please conserve bandwidth. If you are the last person to leave, kindly lock the room.
Please join us for a welcoming barbecue (or braai, as we call it in South Africa) on Wednesday evening 19:00 at the botanical gardens.
Lunch is served daily at Die Bloukamer restaurant on the top floor of the Neelsie student centre.
Conference Dinner (Thursday evening)
The conference dinner is held on Thursday evening at 19:00 at the Clos Malverne wine estate. Please meet in front of the conference venue at 18:45 if you require transport.
Directions to GPS coordinates: S33°54.67 E18°48.810
• Drive down the Adam Tas road (the one that leads to Spier) towards Cape Town.• Drive over Adam Tas bridge, and cross the traffic light with the big white arches on your left.• A woodmill appears on the right. After the mill, turn right and follow the roadwork signs that say
"detour", untill you turn left onto the Devon Valley road.• Follow the road for a couple of kilometres and turn left at the Clos Malverne sign.• The wine farm is straight ahead, on your right, just before the top of the hill.
Programme for SANUM 2011
Time Wednesday 23 March Thursday 24 March Friday 25 March
08:15—09:00 Registration (Van der Sterr building)
09:00—10:00
Cha
ir: W
eide
man Plenary I (Room 1052)
Cha
ir: H
erbs
t Plenary I (Room 1052)
Cha
ir: L
aurie Plenary I (Room 1052)
Nick TrefethenSix myths of polynomial interpolation and quadrature
Desmond HighamModels and Algorithms for Evolving Networks
Nick TrefethenIntroduction to Chebfun Computing
10:00—10:30 Tea
10:30—11:30
Cha
ir: W
eide
man
Plenary II
Cha
ir: H
erbs
t
Plenary II
Cha
ir: M
ason Plenary II
Mike PowellAn inverse matrix for optimization without derivatives
Jared TannerCompressed Sensing: Theory and Software
Douw SteynModelling approaches to understanding the
dynamics and kinematics of sea breezes
11:30—12:00 Room 1052C
hair:
Her
bst
Room 1053 Room 1052
Cha
ir: M
ahom
ed
Room 1053
Cha
ir: M
oits
heki
Room 1052
Cha
ir: K
ara
Room 1053
DragomirQuadrature Rules for the Riemann-Stieltjes Integral
and Applications
Barashenkov Rocking modes of the
sine-Gordon and4 kinks
De PierroOptimization,
Compressed Sensing and Computed Tomography
BandaRelaxation Schemes for Nonlinear Partial
Differential Equations
BahRIC bounds and aysmptotics for
Gaussian random matrices
ObaidAnalysis of an HIV
model with a distributed delay and behavioral
change
12:00—12:30De la Hoz
Two-Dimensional Advection-Diffusion,
Differentiation Matrices and Sylvester Systems
AlexeevaAnisotropic solitons in
the "subdiffractive" NLS on the plane
Fabris-RotelliLULU Theory, the
DPT and Scale-Space Theory
UoaneA stability notion for
Shallow Water Lattice Boltzmann Equation
EneyewMethods for
Solving Shifted Linear Systems
with Application to Linear Parabolic
PDEs
SidahmedComputational
methods for option pricing problems on non-dividend paying assets
12:30—14:00 Lunch
14:00—14:30
Cha
ir: M
akin
de
MasonThin slender rivulet on a
porous substrate
Cha
ir: P
atid
ar
MolchanStability of cnoidal waves
in the parametrically driven nonlinear
Schroedinger equation
SANUM General Meeting
See http://dip.sun.ac.za/sanum for more information.
14:30—15:00
Abelman Stokes's first problem for a rotating Sisko fluid with
porous space
WeidemanA Numerical
Methodology for the Painlevé Equations A
belm
an
ElsheikhThe effect of a
distributed delay on the transmission
dynamics of malaria V. R
ensb
urg Ngnotchouye
Particle Methods for the Solution of
Nonclassical Systems of Conservation Laws
15:00—15:30 Tea
15:30—16:00
Cha
ir: B
anda
MoitshekiTransient heat transfer in longitudinal fin of various profiles with temperature-
dependent thermal conductivity
Cha
ir: L
aurie
Van RensburgSolvability of a model for the vibration of a beam with a damping tip body
Cha
ir: A
belm
an
KhabirSolving option pricing problems using spline
techniques
Cha
ir: V
. Ren
sbur
g
KaraConservation laws
and conserved quantities of systems
of PDEs
16:00—16:30 HarleyNumerical investigation of a steady heat transfer in a longitudinal fin of various
profiles
BassonConvergence of the finite element approximation
for the vibration of a Timoshenko beam
AkanbiApplication of a
geometric explicit Runge-Kutta method to Pharmacokinetic
models
MahomedLaplace-Type Semi-
Invariants for a System of Two Linear Parabolic Equations
16:30—17:00 MakindeNumerical investigation of
unsteady MHD thermal boundary layer over a stretching sheet with a
convective surface boundary condition
LayeniAn atypical re-presentation of
Goodman's profile and a Stefan problem
MtemeriNumerical methods
for singularly perturbed problems
having discontinuous source terms
PototskyEnhanced rectification of attracting particles
in a single-file
17:00—17:30 OlayiwolaNumerical Solutions of Generalized Burger’s-Huxley Equation by Modified Variational
Iteration Method
BakheetDynamics of the Non-
autonomous Owen-Smith Model
MunyakaziApplication of
numerical singular perturbation methods to solve some cross-diffusion models in
biology
DuttaNumerical Algorithm to Solve Nonlinear
Hyperbolic Equations to Simulate Parallel
Channel Instability in Boiling Water Nuclear
Reactors
19:00— Welcoming Reception Conference Dinner
6
Wednesday 23 March
WEDNESDAY PLENARY (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . . 7
Six myths of polynomial interpolation and quadratureProf. Nick Trefethen, Oxford University . . . . . . . . . . . . . . . . . . . . . . . . 7
An inverse matrix for optimization without derivativesProf. Michael Powell, University of Cambridge . . . . . . . . . . . . . . . . . . . . 7
WEDNESDAY MORNING I (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . 7
Quadrature Rules for the Riemann-Stieltjes Integral and ApplicationsProf. Sever Silvestru Dragomir, University of the Witwatersrand . . . . . . . . . . 7
Two-Dimensional Advection-Di�usion, Di�erentiation Matrices and Sylvester SystemsDr Francisco De la Hoz, University of the Basque Country . . . . . . . . . . . . . 7
WEDNESDAY MORNING II (ROOM 1053) . . . . . . . . . . . . . . . . . . . . . . . 7
Rocking modes of the sine-Gordon and φ4 kinksProf. Igor Barashenkov, University of Cape Town . . . . . . . . . . . . . . . . . . . 8
Anisotropic solitons in the �subdi�ractive� NLS on the planeDr Nora Alexeeva, University of Cape Town . . . . . . . . . . . . . . . . . . . . . . 8
WEDNESDAY AFTERNOON I (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . 8
Thin slender rivulet on a porous substrateProf. David Paul Mason, University of the Witwatersrand . . . . . . . . . . . . . . 8
Stokes' �rst problem for a rotating Sisko �uid with porous spaceProf. Shirley Abelman, University of the Witwatersrand . . . . . . . . . . . . . . . 8
WEDNESDAY AFTERNOON II (ROOM 1053) . . . . . . . . . . . . . . . . . . . . . 8
Stability of cnoidal waves in the parametrically driven nonlinear Schroedinger equationDr Max Molchan, University of Cape Town . . . . . . . . . . . . . . . . . . . . . . 8
A Numerical Methodology for the Painlevé EquationsProf. André Weideman, Stellenbosch University . . . . . . . . . . . . . . . . . . . . 8
WEDNESDAY AFTERNOON III (ROOM 1052) . . . . . . . . . . . . . . . . . . . . 8
Transient heat transfer in longitudinal �n of various pro�les with temperature-dependentthermal conductivityDr Raseelo Joel Moitsheki, University of the Witwatersrand . . . . . . . . . . . . . 9
Numerical investigation of a steady heat transfer in a longitudinal �n of various pro�lesDr Charis Harley, University of the Witwatersrand . . . . . . . . . . . . . . . . . . 9
Numerical investigation of unsteady MHD thermal boundary layer over a stretching sheetwith a convective surface boundary conditionProf. Oluwole Daniel Makinde, Cape Peninsula University of Technology . . . . . 9
Numerical Solutions of Generalized Burger's-Huxley Equation by Modi�ed Variational It-eration MethodMorufu Oyedunsi Olayiwola, Dept. of Mathematical & Physical Sciences, Osun
State University Osogbo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
WEDNESDAY AFTERNOON IV (ROOM 1053) . . . . . . . . . . . . . . . . . . . . 10
Solvability of a model for the vibration of a beam with a damping tip bodyProf. Nic Janse van Rensburg, University of Pretoria . . . . . . . . . . . . . . . . 10
Convergence of the �nite element approximation for the vibration of a Timoshenko beamMadelein Basson, University of Pretoria . . . . . . . . . . . . . . . . . . . . . . . . 10
An atypical re-presentation of Goodman's pro�le and a Stefan problemDr Olawanle Layeni, University of Cape Town . . . . . . . . . . . . . . . . . . . . 10
Dynamics of the Non-autonomous Owen-Smith ModelMohamed Bakheet, University of Cape Town . . . . . . . . . . . . . . . . . . . . . 10
Wednesday Morning II (Room 1053) 7
SIX MYTHS OF POLYNOMIALINTERPOLATION AND QUADRA-TURE
Prof. Nick Trefethen (Oxford University)
Computation with polynomials is a powerful tool forall kinds of numerical problems, but the subject hasbeen held back by longstanding confusion on a num-ber of key points. In this talk I'll attempt to sortthings out as systematically as possible by focusingon six widespread misconceptions. In each case I willexplain how the myth took hold � for all of themcontain some truth � and then I'll give theorems andnumerical demonstrations to show why it is mostlyfalse.
AN INVERSE MATRIX FOR OP-TIMIZATION WITHOUT DERIVA-TIVES
Prof. Michael Powell (University of Cambridge)
A simple way of estimating the gradient of a functionF (y) of n variables is to calculate F at n + 1 non-degenerate points yi, i = 0, 1, . . . , n, say, and to pickthe gradient of the linear function that interpolatesthe values F (yi), i = 0, 1, . . . , n. The nondegeneracycondition is that the volume of the convex hull of thepoints in n dimensions is nonzero. In other words,the n × n matrix Y that has the columns (yi − y0),i = 1, 2, . . . , n, is required to be nonsingular, where,for convenience, the ordering of the points makesF (y0) the greatest of the values F (yi), i = 0, 1, . . . , n.We consider the inverse of Y .This setting occurs in some iterative algorithms forthe unconstrained maximization of F , the estimatedgradient being used as a search direction from y0,which leads to a new interpolation point that replacesone of the old ones. Then Y and its inverse are up-dated for the next iteration. Similar replacementsand updates are made on other iterations, where thenew interpolation point is chosen to maintain an ade-quate volume of the convex hull, or to remove a pointthat is far from y0. It is shown that the presence ofthe inverse matrix allows all the routine operationsof each iteration to take only of magnitude n squaredoperations, which is important when n is large.The n + 2 values of F that are available when a re-placement is made provide one piece of second deriva-tive information. Thus, without calculating any morevalues of F , the data F (yi), i = 0, 1, . . . , n, of the nextiteration are interpolated by a very crude quadraticpolynomial instead of by a linear one, the quadraticbeing produced by the �symmetric Broyden formula�.We �nd that our inverse matrix allows this taskalso to be completed in only of order n2 operations.
Some numerical results demonstrate that the use ofthese quadratic polynomials instead of linear ones canincrease greatly the e�ciency of optimization algo-rithms.
QUADRATURE RULES FOR THERIEMANN-STIELTJES INTEGRALAND APPLICATIONS
Prof. Sever Silvestru Dragomir (University of theWitwatersrand)
Some quadrature rules for the Riemann-Stieltjes in-tegral via the Ostrowski, Trapezoidal and Gruss'type inequalities are presented. Sharp a priory er-ror bounds and applications in approximating con-tinuous functions of selfadjoint operators in Hilbertspaces are given as well.
TWO-DIMENSIONAL ADVECTION-DIFFUSION, DIFFERENTIATIONMATRICES AND SYLVESTER SYS-TEMS
Dr Francisco De la Hoz (University of the BasqueCountry)
In this talk we describe a spectrally accurate, un-conditionally stable, e�cient method using opera-tional matrices to solve numerically two-dimensionaladvection-di�usion equations on a rectangular do-main at any arbitrarily large time, relating PDE'sand Sylvester-type equations.
ROCKING MODES OF THE SINE-GORDON AND φ4 KINKS
Prof. Igor Barashenkov (University of Cape Town)
The present study has been motivated by an ongo-ing debate on the existence of the internal mode ofthe sine-Gordon kink, the so-called Rice mode. Thespectrum of linear excitations of the sine-Gordon kinkdoes not include localised modes other than transla-tions; however, a rocking motion of the kink is ob-served numerically and is reasonably accurately re-produced in collective-coordinate approximations.Here, the rocking kinks are studied using a singu-lar perturbation expansion combining collective co-ordinates of the excited kink with a hierarchy ofspace and time scales. We show that despite nothaving any discrete internal modes, the sine-Gordonkink may perform an osciilatory motion very simi-lar to the one occurring when a discrete mode is ex-cited. This localised rocking motion involves contin-uous spectrum of the kink. The amplitude of therocking mode is shown to satisfy the (self-focusing)
8 Wednesday 23 March
nonlinear Schrödinger equation with a nonhomoge-neous boundary condition at the origin.The φ4 kink is also shown to perform a rocking mo-tion � in addition to the well familiar wobblingmode.
ANISOTROPIC SOLITONS IN THE�SUBDIFFRACTIVE� NLS ON THEPLANE
Dr Nora Alexeeva (University of Cape Town)
The periodic microscopic modulation of the exter-nal potential in optical and atomic systems resultsin a macroscopic modi�cation of the net di�ractionof wave packets. In particular, the envelopes ofthe Bloch modes satisfy the �subdi�ractive" nonlin-ear Schroedinger equation on the plane: the cubicNLS combining second- and forth-order derivatives.We construct anisotropic soliton-like solutions of thisequation and analyze their stability properties.
THIN SLENDER RIVULET ON APOROUS SUBSTRATE
Prof. David Paul Mason (University of the Witwa-tersrand)
A rivulet is a thin three-dimensional �uid �lm which�ows down an inclined plane under gravity. The �uidis incompressible and Newtonian and the �ow is un-steady with leak-o� into the plane. Using the thin�lm approximation and assuming a slender rivulet asecond order partial di�erential equation in one timeand two spatial variables is derived. Using scalingtransformations the partial di�erential equation is re-duced in two steps to an ordinary di�erential equa-tion.Numerical solutions are derived. It is found thatthe width of the rivulet decreases as time increases.The e�ect of �uid leak-o� on the rivulet is investi-gated.
STOKES' FIRST PROBLEM FORA ROTATING SISKO FLUID WITHPOROUS SPACE
Prof. Shirley Abelman (University of the Witwater-srand)
Unsteady �ow of a Sisko �uid induced by a sud-denly moved in�nite plate is investigated in a rotatingframe. The �uid occupying the porous half space iselectrically conducting in the presence of a variablemagnetic �eld. Conservation laws of mass and mo-mentum are utilised in the derivation of the di�eren-tial equation. The modi�ed Darcy's law is employed
in the problem development. The governing non- lin-ear problem is solved numerically. The e�ects of var-ious parameters of interest on the velocity pro�le areshown explicitly.
STABILITY OF CNOIDALWAVES IN THE PARAMETRI-CALLY DRIVEN NONLINEARSCHROEDINGER EQUATION
Dr Max Molchan (University of Cape Town)
We study the linear stability of cnoidal wave-solutionsof the parametrically driven, damped nonlinearSchroedinger equation. Out of two cn- and two dn-waves, two waves are shown to be unstable for allvalues of the driver's strength, dissipation and spa-tial period. We analytically and numerically estab-lish that in the long wavelength limit the remainingcn type wave is stable if the driver's strength andthe dissipation are small enough, while the dn-waveis unstable with respect to arbitrary quasi-periodicperturbations for all values of the governing parame-ters. We numerically investigate stability propertiesof cnoidal waves for di�erent values of the spatial pe-riod for all values of the driver's strength and dissipa-tion and discuss their temporal evolution dynamics.
A NUMERICAL METHODOLOGYFOR THE PAINLEVÉ EQUATIONS
Prof. André Weideman (Stellenbosch University)
We present a numerical methodology for the Painlevéequation, and demonstrate its performance on the PIequation. The key ingredient is that, in order to pre-serve numerical stability, di�erent numerical methodsare used in di�erent regions of the complex plane. Inthe regions containing poles, the algorithm uses localPadé approximations combined with an initial-valuestepping strategy that goes around the poles. In thesmooth regions, a Chebyshev collocation method isused as a boundary-value solver. In the talk we re-port on the performance of the algorithm, and presentsolutions with fascinating pole �eld patterns that webelieve have not been observed before. (Joint workwith Bengt Fornberg.)
TRANSIENT HEAT TRANSFER INLONGITUDINAL FIN OF VARIOUSPROFILES WITH TEMPERATURE-DEPENDENT THERMAL CONDUC-TIVITY
Dr Raseelo Joel Moitsheki (University of the Witwa-tersrand)
Wednesday Afternoon III (Room 1052) 9
Unsteady heat transfer through a longitudinal �n ofvarious pro�les is studied. Thermal conductivity andheat transfer coe�cient are assumed to be temper-ature dependent. The resulting partial di�erentialequation (PDE) is highly nonlinear. Classical Liepoint symmetry methods are employed and some re-ductions are performed. In the case of the concaveparabolic �n, the boundary conditions are invariantunder the obtained symmetry at initial state. Thegoverning boundary value problems (BVP) are solvednumerically. The e�ects of the realistic �n parametersuch as the thermo-geometric �n parameter and theexponent of the heat transfer coe�cient on tempera-ture distribution are studied.
NUMERICAL INVESTIGATION OFA STEADY HEAT TRANSFER IN ALONGITUDINAL FIN OF VARIOUSPROFILES
Dr Charis Harley (University of the Witwatersrand)
In this paper we consider a longitudinal �n with rect-angular, triangular, concave and convex parabolicpro�les attached to a stationary base surface. Theheat transfer coe�cient is given as a power law andthe thermal conductivity as a linear function, allow-ing both to be temperature-dependent. Numericalsolutions for the relevant energy balance equationfor a longitudinal �n in dimensionless variables areobtained through the implementation of an in-builtfunction, bvp4c, in MATLAB. Solutions are consid-ered and compared for the mentioned pro�les andvarious values of M and n which provides some usefulinsight into the problem at hand. The phase dia-grams for each case are also considered as a meansof investigating properties of the solutions obtained.This is a signi�cant improvement to the study andconstruction of solutions for longitudinal �ns of var-ious pro�les since, as far as the authors are aware,exact solutions in particular for the concave and con-vex parabolic cases are extremely di�cult to obtain.Another novelty of the work undertaken in this pa-per is the choice of the forms for the heat transfer andthermal conductivity coe�cients. Solutions in knownliterature have predominantly been considered whenthe heat transfer and thermal conductivity coe�cientare both constants.
NUMERICAL INVESTIGATIONOF UNSTEADY MHD THER-MAL BOUNDARY LAYER OVERA STRETCHING SHEET WITH ACONVECTIVE SURFACE BOUND-ARY CONDITION
Prof. Oluwole Daniel Makinde (Cape Peninsula Uni-versity of Technology)
Hydromagnetic thermal boundary layer over a mov-ing surface has an important bearing on several tech-nical applications in engineering and industrial pro-cesses.In this talk, the combined e�ect of magnetic�eld and �ow unsteadiness on thermal boundary layerover a stretching porous sheet with a convective sur-face heat exchange is investigated. By taking suitablesimilarity variables, the governing boundary layerequations are transformed into a set of coupled non-linear ordinary di�erential equations and then tacklednumerically using shooting quadrature. The e�ectsof key parameters on the �uid velocity, temperature,skin friction and Nusselt number in the �ow regimeare depicted graphically and analyzed in detail. Com-parison of numerical results is made with previouslypublished results under the special cases, and foundto be in good agreement.
References
[1] O. D. Makinde: MHD mixed-convection interac-tion with thermal radiation and nth order chemicalreaction past a vertical porous plate embedded in aporous medium. Chemical Engineering Communica-tions, Vol. 198 (4), 590-608, 2011.[2] O. D. Makinde: On MHD heat and mass transferover a moving vertical plate with a convective surfaceboundary condition. Canadian Journal of ChemicalEngineering, Vol. 88, pages 983-990, 2010[3] O. D. Makinde, A. Aziz: MHD mixed convectionfrom a vertical plate embedded in a porous mediumwith a convective boundary condition, InternationalJournal of Thermal Sciences, Vol. 49, 1813-1820,2010.[4] O. D. Makinde: Similarity solution of hydromag-netic heat and mass transfer over a vertical platewith a convective surface boundary condition. In-ternational Journal of Physical Sciences Vol. 5(6),700-710, 2010.[5] O. D. Makinde, P. O. Olanrewaju: Buoyancy ef-fects on thermal boundary layer over a vertical platewith a convective surface boundary condition. Trans-action of ASME �Journal of Fluid Engineering, Vol.132, 044502(1-4), 2010.
10 Wednesday 23 March
NUMERICAL SOLUTIONS OF GEN-ERALIZED BURGER'S-HUXLEYEQUATION BY MODIFIED VARIA-TIONAL ITERATION METHOD
Morufu Oyedunsi Olayiwola (Dept. of Mathematical& Physical Sciences, Osun State University Osogbo)
Numerical solutions of the generalized Burger's-Huxley are obtained using a Modi�ed VariationalIteration Method (MVIM) with minimal computa-tional e�orts. The computed results with this tech-nique have been compared with other results. Thepresent method is seen to be a very reliable alter-native method to some existing techniques for suchnonlinear problems.
SOLVABILITY OF A MODEL FORTHE VIBRATION OF A BEAMWITH A DAMPING TIP BODY
Prof. Nic Janse van Rensburg (University of Preto-ria)
We consider a model for the vibration of a beam witha damping tip body that appeared in a recent article.In this talk we derive a variational form for the mo-tion of the beam and use it to prove that the modelproblem has a unique solution. Di�erent cases areconsidered and the proofs are based on existence re-sults for a general linear vibration model problem (invariational form).
CONVERGENCE OF THE FINITEELEMENT APPROXIMATION FORTHE VIBRATION OF A TIMO-SHENKO BEAM
Madelein Basson (University of Pretoria)
We consider a model problem for the vibration of aTimoshenko beam with boundary damping. Using aso called standard energy method, we prove that theGalerkin approximation converges to the solution andderive error estimates.
AN ATYPICAL RE-PRESENTATIONOF GOODMAN'S PROFILE AND ASTEFAN PROBLEM
Dr Olawanle Layeni (University of Cape Town)
Due to its extreme simplicity the heat balance in-tegral method (HBIM), introduced by Goodman foraddressing transport problems, has attracted lots ofattention in recent times. In particular, the subtle ob-jective of most of these have been that of signi�cant
improvement of its accuracy while retaining simplic-ity. A crucial factor in achieving this is the choiceof test functions/pro�les, of which holds little struc-ture in current literature. It is shown, by elemen-tary methods, how seemingly disjoint sets of earlierpro�ered pro�les relate. Further, selected pertinentgenerators, leading to novel test pro�les, are intro-duced and observed to yield remarkably accurate ap-proximate solutions to a benchmark Stefan (melting)problem.
DYNAMICS OF THE NON-AUTONOMOUS OWEN-SMITHMODEL
Mohamed Bakheet (University of Cape Town)
We study the dynamics of the general non-autonomous case of Owen-Smith metaphysiologicalmodel, to explore the e�ects of seasonality on popu-lation �uctuations. The study will include the perma-nence, herbivore extinction, global asymptotic stabil-ity and existence of positive periodic solutions. Un-der certain assumptions, we obtained su�cient andnecessary conditions for the permanency of the sys-tem. And also we obtained a su�cient condition forexistence of periodic solutions.
Wednesday 23 March 11
Thursday 24 March
THURSDAY PLENARY (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Models and Algorithms for Evolving NetworksProf. Desmond Higham, University of Strathclyde . . . . . . . . . . . . . . . . . . 12
Compressed Sensing: Theory and SoftwareProf. Jared Tanner, University of Edinburgh . . . . . . . . . . . . . . . . . . . . . 12
THURSDAY MORNING I (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . . 12
Optimization, Compressed Sensing and Computed TomographyProf. Alvaro De Pierro, University of Campinas . . . . . . . . . . . . . . . . . . . 12
LULU Theory, the DPT and Scale-Space TheoryInger Fabris-Rotelli, University of Pretoria . . . . . . . . . . . . . . . . . . . . . . 12
THURSDAY MORNING II (ROOM 1053) . . . . . . . . . . . . . . . . . . . . . . . . 12
Relaxation Schemes for Nonlinear Partial Di�erential EquationsProf. Mapundi Banda, Wits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
A stability notion for Shallow Water Lattice Boltzmann EquationTumelo Uoane, Wits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
THURSDAY AFTERNOON I (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . 13
The e�ect of a distributed delay on the transmission dynamics of malariaSara Elsheikh, University of the Western Cape . . . . . . . . . . . . . . . . . . . . 13
Solving option pricing problems using spline techniquesMohmed Khabir, University of the Western Cape . . . . . . . . . . . . . . . . . . . 13
Application of a geometric explicit Runge-Kutta method to Pharmacokinetic modelsDr Moses Adebowale Akanbi, University of the Western Cape . . . . . . . . . . . . 13
Numerical methods for singularly perturbed problems having discontinuous source termsNyika Mtemeri, University of the Western Cape . . . . . . . . . . . . . . . . . . . . 13
Application of numerical singular perturbation methods to solve some cross-di�usion mod-els in biologyDr Justin B. Munyakazi, University of the Western Cape . . . . . . . . . . . . . . 13
THURSDAY AFTERNOON II (ROOM 1053) . . . . . . . . . . . . . . . . . . . . . . 13
Particle Methods and non Dissipative Central Upwind schemes for the Solution of Non-classical Systems of Conservation LawsDr Jean Medard T. Ngnotchouye, University of kwaZulu-Natal . . . . . . . . . . . 14
Conservation laws and conserved quantities of systems of PDEsProf. Abdul Kara, University of the Witwatersrand . . . . . . . . . . . . . . . . . . 14
Laplace-Type Semi-Invariants for a System of Two Linear Parabolic EquationsProf. Fazal Mahomed, Wits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Enhanced recti�cation of attracting particles in a single-�leDr Andrey Pototsky, University of Cape Town . . . . . . . . . . . . . . . . . . . . 14
Numerical Algorithm to Solve Nonlinear Hyperbolic Equations to Simulate Parallel Chan-nel Instability in Boiling Water Nuclear ReactorsDr Goutam Dutta, IIITDM Jabalpur . . . . . . . . . . . . . . . . . . . . . . . . . . 15
12 Thursday 24 March
MODELS AND ALGORITHMS FOREVOLVING NETWORKS
Prof. Desmond Higham (University of Strathclyde)
The digital revolution is generating novel large scaleexamples of connectivity patterns that change overtime; this scenario may be formalized as a graph witha �xed set of nodes whose edges switch on and o�.For example, we may have networks of interactingmobile phone users, emailers, Facebookers or Tweet-ers. To understand and quantify the key propertiesof such evolving networks, we can extend classicalgraph theoretical notions like degree and pathlength,and more general network science concepts such ascentrality, to the dynamic setting.In this talk I will focus on linear algebra-based ideasand show that computations based on matrix prod-ucts can capture various aspects of information �owaround an evolving network. Illustrative exampleswill be given for both synthetic and real-world datasets. I will also look at the issue of modeling this typeof network evolution.
COMPRESSED SENSING: THEORYAND SOFTWARE
Prof. Jared Tanner (University of Edinburgh)
Compressed Sensing is a new data acquisition tech-nique by which data can be sampled at the rate of itsinformation content rather than the ambient dimen-sion of the data. In special cases, precise samplingtheorems have been derived, explaining the exact be-havior of compressed sensing algorithms. However,for many algorithms, the sampling theorems are woe-fully pessimistic. We review the precise sampling the-orems and show how a GPU based software packageallows us to accurately calculate sampling theoremsfor other algorithms. This work is joint with DavidL. Donoho and Je�rey D. Blanchard.
OPTIMIZATION, COMPRESSEDSENSING AND COMPUTED TO-MOGRAPHY
Prof. Alvaro De Pierro (University of Campinas)
Compressed Sensing (CS) is a new area of intenseresearch in applied mathematics. For many impor-tant applications it allows to �nd the unique sparsesolution of a very large underdetermined system oflinear equations through l1 minimization. In the caseof imaging, l1 is replaced by Total Variation (TV). Ifapplicable in Computed Tomography, it would meanfaster acquisition protocols and/or less radiation ex-posure for the patient. In this work we describe howold methods in Tomography could be adapted and
generalized [1] for their application in the new CSsetting. We also describe how this approach couldbe useful for estimating the associated regularizationparameters [2] and we apply it to Single Photon Emis-sion Computed Tomography (SPECT) data.
References
[1] E.S. Helou and A.R. De Pierro, Incremental sub-gradients for constrained convex optimization: a uni-�ed framework and new methods SIAM J. Optimiza-tion, 20, 3, 1547-1572, 2010.[2] E.S. Helou and A.R. De Pierro, On PerturbedSteepest Descent Methods with Inexact Line Searchfor Bilevel Convex Optimization Optimization 60, 8,2011.
LULU THEORY, THE DPT ANDSCALE-SPACE THEORY
Inger Fabris-Rotelli (University of Pretoria)
The DPT is the repeated application of the LULUoperators Ln and Un. The resulting decompositionof an image provides a nonlinear scale-space, whichwe call the LULU scale-space. A formal setting andtheory will now be provided for this new scale-space.Possible applications in image analysis will also bediscussed.
RELAXATION SCHEMES FORNONLINEAR PARTIAL DIFFER-ENTIAL EQUATIONS
Prof. Mapundi Banda (Wits)
A family of relaxation schemes for nonlinear partialdi�erential equations will be presented. The schemescan achieve high-order of accuracy and give non-oscillatory solutions even in the presence of singu-larities. Test results for One- and two-dimensionalresults will be discussed.
A STABILITY NOTION FOR SHAL-LOW WATER LATTICE BOLTZ-MANN EQUATION
Tumelo Uoane (Wits)
Lattice Boltzmann (LB) equations are used as an al-ternative numerical formulation to simulate shallowwater equations (SWEs). Hence, numerical stabilityof the method was investigated. The stability struc-ture will be used as a guideline to determine the sta-bility of LB equations applied to SWEs. For instantsome of the parameters in the LB equations are ad-justed based on the stability structure. With thismethod, stable LB models are prescribed.
Thursday Afternoon II (Room 1053) 13
THE EFFECT OF A DISTRIBUTEDDELAY ON THE TRANSMISSIONDYNAMICS OF MALARIA
Sara Elsheikh (University of the Western Cape)
We consider a vector-host model for the transmissiondynamics of malaria with a gamma distributed delay.We analyze the impact of the delay on the steadystates and their stability and determine a thresholdvalue for the mean delay at which the system under-goes either a transcritical or a backward bifurcation.A sensitivity analysis is performed to compare the ef-fect of the mean delay and shape parameter on theinitial disease transmission and the disease prevalenceat the equilibrium. Numerical simulations are carriedout to con�rm the theoretical �ndings to investigatethe impact of the delay on the prevalence of the dis-ease.This is joint work with R. Oui�ki and K.C. Patidar.
SOLVING OPTION PRICING PROB-LEMS USING SPLINE TECH-NIQUES
Mohmed Khabir (University of the Western Cape)
In this talk we discuss construction and analysis of anumerical method for solving nonlinear Black-Scholespartial di�erential equation modelling European op-tions. The governing equation is a di�usion prob-lem. We use implicit time-stepping method togetherwith the B-spline collocation method. The proposedmethod is unconditionally stable and has good con-vergence properties. The computational performanceof the proposed method is compared with those ob-tained by using other methods.This is joint work with K.C. Patidar.
APPLICATION OF A GEOMET-RIC EXPLICIT RUNGE-KUTTAMETHOD TO PHARMACOKINETICMODELS
Dr Moses Adebowale Akanbi (University of the West-ern Cape)
Many physical phenomena are modeled by means ofdi�erential equations. In most cases, these equationsare too complex to be solved exactly. In this talk wewill brie�y discuss the underlying theory of geomet-ric explicit Runge-Kutta method. We then apply thisapproach to solve some mathematical models arisingin Pharmacokinetics.This is joint work with K.C. Patidar.
NUMERICAL METHODS FOR SIN-GULARLY PERTURBED PROB-LEMS HAVING DISCONTINUOUSSOURCE TERMS
Nyika Mtemeri (University of the Western Cape)
In this talk, we consider a class of singularly per-turbed problems with discontinuous source term. Weprovide some qualitative results on the solution ofthese problems. We then present a robust numericalmethod mimicking some of these qualitative proper-ties along with some comparative numerical results.This is joint work with J.B. Munyakazi and K.C. Pati-dar.
APPLICATION OF NUMERICALSINGULAR PERTURBATIONMETHODS TO SOLVE SOMECROSS-DIFFUSION MODELS INBIOLOGY
Dr Justin B. Munyakazi (University of the WesternCape)
Cross-di�usion models are being used to study var-ious phenomena including in biology, epidemiologyand medicine. Numerous nonlinear and complex dy-namics have been observed in these models whichcan help to better understand the more challengingenvironmental and health problems such as pollu-tion, invasion of species, emerging of new diseasesand surging of the existing ones. While a vast litera-ture presents qualitative investigations of such mod-els, very little quantitative work has been done todate. Usually these models are highly nonlinear andinvolve large systems of di�erential equations, thusputting a real challenge to solve them analytically.It is therefore imperative to seek robust numericalmethods for their solutions. In this talk we re-view some of these models that arise in biology. Wethen show how the methods developed for singularlyperturbed reaction-di�usion problems can be used tosolve these cross-di�usion models.This is joint work with K.C. Patidar.
PARTICLE METHODS AND NONDISSIPATIVE CENTRAL UPWINDSCHEMES FOR THE SOLUTIONOF NONCLASSICAL SYSTEMS OFCONSERVATION LAWS
Dr Jean Medard T. Ngnotchouye (University ofkwaZulu-Natal)
In this talk, we review and compare two di�erentnumerical schemes for the solution of nonclassical
14 Thursday 24 March
system of conservation laws. Our interest is in theparticle method of Chertock et Kurganov and thenon dissipative Central Upwind scheme of Kurganovand Lin. Our investigations show that the particlemethod depends heavily on the recovery procedurewhile the Central-Upwind scheme give poor resolu-tion of the delta-shocks. An hybridization of thesemethods is considered. We present numerical resultsrelated to applications in pressureless gas dynamics.
CONSERVATION LAWS AND CON-SERVED QUANTITIES OF SYS-TEMS OF PDES
Prof. Abdul Kara (University of the Witwatersrand)
The conserved quantities of systems of PDEs are sig-ni�cant in the study of the systems as they indicatethe validity of solutions that are obtained by someapproach. This is particularly useful in the case ofnumerical approaches. We develop a procedure to de-termine the conserved densities for a number of wellknown scalar PDEs and systems of PDEs and deter-mine conserved quantities for soliton like solutions.
LAPLACE-TYPE SEMI-INVARIANTS FOR A SYSTEMOF TWO LINEAR PARABOLICEQUATIONS
Prof. Fazal Mahomed (Wits)
We obtain new semi-invariants for a system of twolinear parabolic partial di�erential equations (PDEs)in two independent variables under equivalence trans-formations of the dependent variables only. This isachieved for a class of systems of two linear parabolicPDEs that correspond to a scalar complex linear(1+1) parabolic equation. The complex transforma-tions of the dependent variables which map the com-plex scalar linear parabolic PDE to itself provide uswith real transformations that map the correspond-ing system of linear parabolic PDEs to itself with dif-ferent coe�cients in general. The semi-invariants de-duced for this class of systems of two linear parabolicequations correspond to the complex semi-invariantsof the complex scalar linear parabolic equation. Wealso look at particular cases of the system of parabolicequations when they are uncoupled or coupled in aspecial manner. Moreover, we address the inverseproblem of when systems of linear parabolic equa-tions arise from analytic continuation of a scalar lin-ear parabolic PDE. Examples are given to illustratethe method implemented.
ENHANCED RECTIFICATION OFATTRACTING PARTICLES IN ASINGLE-FILE
Dr Andrey Pototsky (University of Cape Town)
We study the recti�cation current of a single-�le ofattracting particles subjected to a low frequency acdrive and a static ratchet-like potential. Dilute orweakly attracting particles are evenly spread amongthe local minima of the ratchet potential, their jumpsinto the neighboring wells being randomly activatedby noise and drive, with a bias in a preferred direction(ratchet mechanism). We show that increasing theparticle attraction leads to the formation of a con-densed mode, where the particles move as a wholefollowing the ac drive. As a result, the ensuing netparticle current may be one order of magnitude largerthan for dilute or weakly attracting particles.
NUMERICAL ALGORITHM TOSOLVE NONLINEAR HYPERBOLICEQUATIONS TO SIMULATE PAR-ALLEL CHANNEL INSTABILITYIN BOILING WATER NUCLEARREACTORS
Dr Goutam Dutta (IIITDM Jabalpur)
A numerical model is developed to solve nonlinear si-multaneous equations to analyze two-phase �ow boil-ing in vertical channels of the Boiling Water Nu-clear Reactor core. The numerical model takes intoaccount mass, momentum and energy conservationequations to simulate �ow dynamics phenomena andclassi�es the set of equations as hyperbolic in nature.The model �rst transforms conservative form of thepartial di�erential equations into primitive form andthen into characteristic form and then �nally solvesthem in time domain in Eulerian frame of referencewith a characteristic based approach. The numeri-cal algorithm is an e�cient method because it takesinto consideration of the compressibility e�ect of two-phase �ow dynamics, it treats the boundary condi-tions naturally and it provides adequate accuracywith reasonable time in comparison to the methodof characteristics technique which is considered to bebenchmark solution while solving similar problems.The numerical model is next extended to analyzedensity wave oscillations in boiling reactor core andit simulates parallel channel instability of the reac-tor core undergoing both in-phase and out-of- phasemodes of oscillations. The present paper providesthe mathematical support to determine the bound-ary conditions to be imposed while simulating bothin-phase and out-of-phase modes of instabilities andde�nes them explicitly so that one can simulate the
Thursday Afternoon II (Room 1053) 15
parallel channel instability with such numerical algo-rithms. The model is then extended to investigate thee�ect of asymmetric power distribution in two halvesof the reactor core in the context of reactor stabil-ity. Extensive numerical investigations are being car-ried out to determine whether the reactor instabilitywhen undergoing out-of-phase mode of oscillations isgoing to be enhanced or suppressed when subjectedto asymmetric power distribution in comparison tothe symmetric power distribution keeping the totalpower and mass �ow rate same for both the cases.Analysis of asymmetric power distribution on the re-actor instability will help in simulating the reactorwith the present numerical model for more realisticoperating conditions.
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Friday 25 March
FRIDAY PLENARY (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Introduction to Chebfun computingProf. Nick Trefethen, Oxford University . . . . . . . . . . . . . . . . . . . . . . . . 17
Sea Breezes: The phenomenon, and some approaches to understanding their dynamics andkinematicsProf. Douw Steyn, The University of British Columbia . . . . . . . . . . . . . . . . 17
FRIDAY MORNING I (ROOM 1052) . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
RIC bounds and aysmptotics for Gaussian random matricesBubacarr Bah, University of Edinburgh . . . . . . . . . . . . . . . . . . . . . . . . . 17
Methods for Solving Shifted Linear Systems with Application to Linear Parabolic PDEsEyaya Birara Eneyew, Stellenbosch University . . . . . . . . . . . . . . . . . . . . . 17
FRIDAY MORNING II (ROOM 1053) . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Analysis of an HIV model with a distributed delay and behavioral changeHasim Obaid, University of the Western Cape . . . . . . . . . . . . . . . . . . . . . 18
Computational methods for option pricing problems on non-dividend paying assetsAbdelmgid Sidahmed, University of the Western Cape . . . . . . . . . . . . . . . . . 18
Friday Morning II (Room 1053) 17
INTRODUCTION TO CHEBFUNCOMPUTING
Prof. Nick Trefethen (Oxford University)
Anyone who uses Matlab (or Octave or Scilab) willenjoy Chebfun, which overloads Matlab commandsfor vectors and matrices to analogous commands forfunctions and operators. In Chebfun, all it takes tosolve a di�erential equation is "backslash". In thisonline talk I'll brie�y describe how Chebfun worksand the growth of the Chebfun project, and thenspend most of the time showing o� the software. Ifyou have a laptop with Matlab, feel free to bring itwith you and play along. Chebfun can be downloadedfrom www.maths.ox.ac.uk/chebfun/, and copies willalso be available on a memory stick. This is jointwork with Toby Driscoll, Nick Hale, and about adozen other members of the Chebfun team.
SEA BREEZES: THE PHE-NOMENON, AND SOME AP-PROACHES TO UNDERSTANDINGTHEIR DYNAMICS AND KINE-MATICS
Prof. Douw Steyn (The University of BritishColumbia)
I will present the phenomena of sea breezes as an idealgeophysical �uid dynamical object of study. I willdescribe the phenomenon, explain some of its moreinteresting features and make an assertion that a par-ticular sea breeze made western civilization a possi-bility! I will then present a simple, linear analyticalmodel of sea breezes due to Bernard Haurwitz andwill show how that work led to a wide range of an-alytical modelling studies. I will introduce the useof atmospheric numerical models as research tools,and will summarize some of my work designed to un-derstand the interplay of forces driving sea breezedynamics, using a fully nonlinear numerical model.I will present empirical scaling laws for sea breezestrength and depth, and will showin how the outputof a numerical model of sea breezes can be used infurther developing sea breeze scaling.
RIC BOUNDS AND AYSMPTOTICSFOR GAUSSIAN RANDOM MATRI-CES
Bubacarr Bah (University of Edinburgh)
The Restricted Isometry Constants (RIC) of a matrixA measures how close to an isometry is the action of Aon vectors with few nonzero entries, measured in theEuclidean norm. Speci�cally, the upper and lower
RIC of a matrix A of size n by N is the maximumand the minimum deviation from unity (one) of thelargest and smallest, respectively, square of singularvalues of all submatrices formed by taking k columnsfrom A. Calculation of the RIC is intractable for mostmatrices due to its combinatorial nature; however,many random matrices typically have bounded RICin some range of problem sizes (k,n,N). We providethe best known bound on the RIC for Gaussian ma-trices, which is also the smallest known bound onthe RIC for any large rectangular matrix. Our re-sults are built on the prior bounds of Blanchard, Car-tis, and Tanner in Compressed Sensing: How sharpis the Restricted Isometry Property?, with improve-ments achieved by grouping submatrices that share asubstantial number of columns. Furthermore, usingasymptotic approximations of RIC bounds we givefurther insight into the order of measurements neces-sary to guarantee exact recovery in Compressed Sens-ing by computing values of the constants in the or-der terms for some key recovery algorithms in Com-pressed Sensing.
METHODS FOR SOLVING SHIFTEDLINEAR SYSTEMS WITH APPLI-CATION TO LINEAR PARABOLICPDES
Eyaya Birara Eneyew (Stellenbosch University)
In several applications shifted linear systems of theform (A - aI)x = b needs to be solved for several val-ues of the parameter a. Often, these linear systemsare large and sparse. In this talk we present e�cientsolutions of these systems by the Krylov subspacemethods. Because of its shift-invariance property,the Krylov subspace method allows one to obtain ap-proximate solutions for all values of the parameter,by generating a single approximation space. Krylovsubspace methods applied to the shifted systems aregenerally slowly convergent and hence precondition-ing is necessary to improve the convergence. The useof shift-invert preconditioning is discussed and nu-merical comparison of the direct sparse solver withthe Krylov subspace methods are presented. As ap-plication we solve a two-dimensional version of theheat equation.
ANALYSIS OF AN HIV MODELWITH A DISTRIBUTED DELAYAND BEHAVIORAL CHANGE
Hasim Obaid (University of the Western Cape)
We consider a mathematical model for the transmis-sion dynamics of HIV that accounts for behavioralchange. The model also includes a distributed delay
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representing the time needed for individuals to reducetheir risky behavior. The impact of the delay on thestability of the steady states as well as on the bifur-cation behavior of the system is studied. Numericalsimulations supporting the theoretical �ndings willbe presented at the conference.This is joint work with R. Ouifki and K.C. Patidar.
COMPUTATIONAL METHODS FOROPTION PRICING PROBLEMS ONNON-DIVIDEND PAYING ASSETS
Abdelmgid Sidahmed (University of the WesternCape)
In this talk we consider some di�erential equationmodels describing options on non-dividend paying as-sets. Our major focus will be on the plain vanilla op-tions, e.g., European and American options. We willdiscuss some computational methods to solve themfollowed by comparative numerical results.This is joint work with K.C. Patidar.
Friday 25 March 19
Participants
Surname First name(s) A�liation E-mail
Abelman Shirley University of the Witwatersrand [email protected]
Akanbi Moses Adebowale University of the Western Cape [email protected]
Alexeeva Nora University of Cape Town [email protected]
Amoako Gordon African Institute for Mathematical Sci-ences
Bah Bubacarr University of Edinburgh [email protected]
Bakheet Mohamed University of Cape Town [email protected]
Banda Mapundi Wits [email protected]
Barashenkov Igor University of Cape Town [email protected]
Basson Madelein University of Pretoria [email protected]
De Kock Erhardt Rabe Stellenbosch University [email protected]
De Pierro Alvaro University of Campinas [email protected]
De la Hoz Francisco University of the Basque Country [email protected]
Dragomir Sever Silvestru University of the Witwatersrand [email protected]
Dutta Goutam IIITDM Jabalpur [email protected]
Elsheikh Sara University of the Western Cape [email protected]
Eneyew Eyaya Birara Stellenbosch University [email protected]
Fabris-Rotelli Inger University of Pretoria [email protected]
Fatokun Johnson Nasarawa State University, Ke� [email protected]
Goldberg Terence University of Cape Town [email protected]
Groenwold Albert Stellenbosch University [email protected]
Harley Charis University of the Witwatersrand [email protected]
Herbst Ben Stellenbosch University [email protected]
Higham Desmond University of Strathclyde [email protected]
Janse van Rensburg Nic University of Pretoria [email protected]
Kara Abdul University of the Witwatersrand [email protected]
Khabir Mohmed University of the Western Cape [email protected]
Khan Safeer Qatar University [email protected]
Laurie Dirk Stellenbosch University [email protected]
Layeni Olawanle University of Cape Town [email protected]
Lee-Thorp James University of Cape Town [email protected]
Mahomed Fazal Wits [email protected]
Makinde Oluwole Daniel Cape Peninsula University of Technology [email protected]
Mason David Paul University of the Witwatersrand [email protected]
Moitsheki Raseelo Joel University of the Witwatersrand [email protected]
Molchan Max University of Cape Town [email protected]
20 Friday 25 March
Mtemeri Nyika University of the Western Cape [email protected]
Muller Neil University of Stellenbosch [email protected]
Munyakazi Justin B. University of the Western Cape [email protected]
Muthivhi Patrick Mutshutshu [email protected]
Obaid Hasim University of the Western Cape [email protected]
Olivier Carel University of Cape Town [email protected]
Patidar Kailash C. University of the Western Cape [email protected]
Pototsky Andrey University of Cape Town [email protected]
Powell Michael University of Cambridge [email protected]
Rahim Mohammad Tariq FAST-NU [email protected]
Ramanantoanina Andriamihaja University of Stellenbosch [email protected]
Sidahmed Abdelmgid University of the Western Cape [email protected]
Steyn Douw The University of British Columbia [email protected]
Swart Albert Stellenbosch University [email protected]
Tanner Jared University of Edinburgh [email protected]
Teneng Dean Tartu University [email protected]
Teodorescu Emil - Adrian Vienna University of Applied Sciences [email protected]
Trefethen Nick Oxford University [email protected]
Uoane Tumelo Wits [email protected]
Useni Paul Nasarawa State Polytechnic, La�a [email protected]
Vadillo Fernando University of the Basque Country [email protected]
Weideman André Stellenbosch University [email protected]
Van der Walt Stéfan Stellenbosch University [email protected]