Investigating Efficiency of Adomian Decomposition Method in Solving Van Der Pol’s Equation Compared to Regular Perturbation Method
Loading...
Date
2018
Authors
Wambugu, Jane Wanjiku
Njenga, John
Gatoto, James
Journal Title
Journal ISSN
Volume Title
Publisher
ijasr
Abstract
Many physical systems are mathematically modeled leading to nonlinear ordinary differential equations or partial differential
equations, raising the need for an effective method for analyzing the mathematical models which provide solutions that conform to
physical problems. The Adomian Decomposition Method (ADM) has been used to solve a wide range of dynamical systems since
its introduction in 1980’s. Nonlinear oscillatory differential equations have been used in modeling many dynamical systems and
they demonstrate many basic properties of nonlinear systems. These equations have been solved using many approximations
methods e.g. Differential transform, perturbation, variation iteration, and Lindstedt methods. This work investigates the efficiency
in the application of ADM versus perturbation method in solving one of the nonlinear oscillatory differential equations, the Van
Der Pol’s equation. For analysis of accuracy, Runge- Kutta fifth order method is used as a comparison criterion and respective
error bounds are obtained. These results will enhance confidence in the application of ADM or perturbation method in solving
nonlinear oscillatory systems.
Description
article
Keywords
adomian decomposition, Perturbation method, van der pol’s equation
Citation
Wanjiku, W. J., Njenga, J., & James, G. Investigating efficiency of Adomian decomposition method in solving van der pol’s equation compared to regular perturbation method.