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

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Soomro, Abdul Sattar
Tularam, Gurudeo
Shaikh, Muhammad Majtaba
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Alexander Decker

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2013
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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. http://www.iiste.org/Journals/index.php/index/search/advancedResults

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Mathematical Theory and Modeling

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3

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2

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© The Author(s) 2013. This is an Open Access article distributed under the terms of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ordinary Differential Equations, Difference Equations and Dynamical Systems

Partial Differential Equations

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