euler modificado vs heun a
TRANSCRIPT
� usando el metodo de Euler Modificado y Heun y comparandolos
Ejercicio b y’=Sent + ã-t , 0 £ t £ 1 , yH0L = 0 con h =1
2
(Debug) In[209]:=
DSolveB:y'@tD �y@tD
t
2
+y@tD
t, y@1D � 1>, y@tD, tF �� Simplify
DSolveBy'@tD �1
tIHy@tDL2
+ y@tDM, y@tD, tF �� Simplify;
(Debug) Out[209]=
::y@tD ® -t
-1 + Log@tD>>
(Debug) In[291]:=
H*usando el metodo de Euler Modificado y Heun y comparandolos
Ejercicio b y'=I y
tM2
+I y
tM , 1£t£2 , yH1L=1 con h=0.1*L
f@t_, y_D := Ky
tO
2
+ Ky
tO
y1@t_D := -t
-1 + Log@tDy1 = 1;
a = 1;
b = 2;
n = 5;
q = SetPrecision;
s = 6;
t0 = 1;
h = 0.1;
we0 = y1;
wh0 = y1;
ForBi = 1, i £ n,
wei = wei-1 +h
2Hf@ti-1, wi-1D + f@ti-1, wei-1 + h * f@ti-1, wei-1DDL;
whi = whi-1 +h
4f@ti-1, wi-1D + 3 * fBti-1 +
2
3h, wi-1 +
2
3h * f@ti-1, wi-1DF ;
yi = y1@ti-1D;
ti = a + i * h;
i++F
TableForm@Table@8q@yi+1, sD, q@wei, sD,
q@Abs@yi+1 - weiD, sD, q@whi, sD, q@Abs@yi+1 - whiD, sD<, 8i, 0, n - 1<D,
TableHeadings ® 8Automatic, 8"Valor real", "Euler Mod.", "Error-Euler Mod"
, "Heun", "Error Heun"<<D
Plot@y1@tD, 8t, a, b<, PlotStyle ® 8Black, Thick<, Epilog ® 88Black, [email protected], Point@Table@8tm, y1@tmD<, 8m, 0, n<DD<,
8Green, [email protected], Point@Table@8tm, wem<, 8m, 0, n<DD<,
8Blue, Line@Table@8tm, y1@tmD<, 8m, 0, n<DD<,
8Red, Line@Table@8tm, wem<, 8m, 0, n<DD<<
DPlot@y1@tD, 8t, a, b<, PlotStyle ® 8Black, Thick<, Epilog ® 8
8Black, [email protected], Point@Table@8tm, y1@tmD<, 8m, 0, n<DD<,
8Green, [email protected], Point@Table@8tm, whm<, 8m, 0, n<DD<,
8Blue, Line@Table@8tm, y1@tmD<, 8m, 0, n<DD<,
8Red, Line@Table@8tm, whm<, 8m, 0, n<DD<<
D
2 Euler MOdificado.nb
(Debug) Out[304]//TableForm=
Valor real Euler Mod. Error-Euler Mod Heun Error Heun1 1.00000 1.00000 0 1.00000 02 1.21589 1.13200 0.0838863 1.00000 0.2158863 1.46757 1.27220 0.195368 1.00998 0.4575934 1.76239 1.42125 0.341138 1.02970 0.7326855 2.10993 1.57969 0.530244 1.05883 1.05110
(Debug) Out[305]=
1.2 1.4 1.6 1.8 2.0
2
3
4
5
6
(Debug) Out[306]=
1.2 1.4 1.6 1.8 2.0
2
3
4
5
6
Euler MOdificado.nb 3