A Comparison of Numerical Methods for Solving the Unforced Van Der Pol’s Equation
File version
Author(s)
Tularam, Gurudeo
Shaikh, Muhammad Majtaba
Griffith University Author(s)
Primary Supervisor
Other Supervisors
Editor(s)
Alexander Decker
Date
Size
1062915 bytes
File type(s)
application/pdf
Location
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
Journal Title
Mathematical Theory and Modeling
Conference Title
Book Title
Edition
Volume
3
Issue
2
Thesis Type
Degree Program
School
Publisher link
DOI
Patent number
Funder(s)
Grant identifier(s)
Rights Statement
Rights Statement
© 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.
Item Access Status
Note
Access the data
Related item(s)
Subject
Ordinary Differential Equations, Difference Equations and Dynamical Systems
Partial Differential Equations