Classical and Higher Order Runge-Kutta Methods with Nonlinear Shooting Technique for Solving Van der Pol (VdP) Equation

Farhana Ahmed Simi, Goutam Saha

Abstract


The goal of the research work is to examine the improvement of numerical solution of VdP equation. The well-known VdP equation is governed by the second order nonlinear ODE and then solved numerically using the classical Runge-Kutta (RK) method, RK-Fehlberg method of order five, Verner method of order eight and Cash-Karp method of order six with nonlinear shooting technique. In this work, numerical simulations have been carried out using NVdP code which is written in MATHEMATICA. Also, the accuracy and efficiency of the solution of VdP equation using different RK methods with nonlinear shooting technique has been investigated. For analysis of accuracy, the approximate exact solution obtained by perturbation method is used for the comparison. It is observed that all the different RK methods give accurate result of the VdP equation. But the classical RK method shows slightly better performance than the other single step techniques.

Keywords


Runge-Kutta, Fehlberg, Verner, Cash-Karp, Shooting method.

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Dhaka University Journal of Science ISSN 1022-2502 (Print) 2408-8528 (Online)