02a persamaan diferensial ordiner 1.pptx
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Persamaan Diferensial Ordiner [Ordinary Differential Equation (ODE)]
Persamaan Diferensial Ordiner[Ordinary Differential Equation (ODE)]Part 1: Euler & Runge Kutta
The sequence of events in the application of ODEs for engineering problem solving. The example is the velocity of a falling parachutist. (Chapra & Canale, 2006)Types of ODEInitial value problemExample:
Boundary value problem Example:
Numerical methods for solving ODEEuler & Modified Euler (IVP)Runge-Kutta (IVP)Shooting method (BVP)Finite difference approximation (BVP)etcEulers methodODE numerical solutionEulers method
Eulers method
Eulers method
Example 1
Example 1, contd.
Example 1, contd.
Example, contd.
Example 1, contd.
Example 1, contd.
Example 1, contd.
Example 1, contd.Eulers method
Improvements of eulers method ODE numerical solutionHeuns method
Heuns method
Graphical depiction of Heuns method. (a) predictor; (b) correctorHeuns methodHeuns method
Example 2
Example 2, contd.
Example 2, contd.
Example 2, contd.The Midpoint Method
The Midpoint Method
Runge-kutta methodODE numerical solutionRunge-Kutta 4th order method
Example 3: Recall the problem in example 1
Example 3, contd.
Example 3, contd.
Example 3, contd.
Example 3, contd.
Example 3, contd.
Example 3, contd.
Example 3, contd.
Example 3, contd.System of equationsODE numerical solutionSystem of equations
Example 4: Eulers method
Example 4, contd.
Example 5: RK method
Example 5, contd.
Example 5, contd.ReferensiChapra, S.E. and Canale, R.P., 2006, Numerical methods for engineers , 5th ed, McGraw Hill, Singapore.Kaw, A. and Barker, C., 2006, http://numericalmethods.eng.usf.edu