A Comparison of Numerical Methods for Solving the Unforced Van Der Pol’s Equation

Abstract

Due to the advancements in the field of computational mathematics, numerical methods are most widely being utilized to solve the equations arising in the fields of applied medical sciences, engineering and technology. In this paper, the numerical solutions of an important equation of applied dynamics: namely, the Unforced Van der Pol’s Equation (UFVDP) are obtained by reducing it to a system of two first order differential equations. The objective of this work is to investigate the efficiency of improved Heun’s (IH) method against the classical Runge-Kutta (RK4) and Mid-point (MP) methods for UFVDP equation. For analysis of accuracy, the Poincare-Lindstedt method has been used as a comparison criterion and respective error bounds are obtained. The results show that the popular RK4 method retains its better accuracy than other methods used for comparison.

Keywords: Van der Pol, Runge-Kutta, Mid-point, Improved Heun’s, Poincare-Lindstedt.