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

Abdul Sattar Soomro, Gurudeo Anand Tularam, Muhammad Mujtaba Shaikh


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.

Full Text: PDF
Download the IISTE publication guideline!

To list your conference here. Please contact the administrator of this platform.

Paper submission email: MTM@iiste.org

ISSN (Paper)2224-5804 ISSN (Online)2225-0522

Please add our address "contact@iiste.org" into your email contact list.

This journal follows ISO 9001 management standard and licensed under a Creative Commons Attribution 3.0 License.

Copyright © www.iiste.org