Solution of Non-Linear Ito System of Equations by Homotopy Analysis Method (HAM)
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Prince Mohammad Bin Fahd University
Online publication date: 2018-04-24
Publication date: 2018-04-24
Eurasian J Anal Chem 2018;13(3):em
Nonlinear Ito system of equations have wide application in applied physics. Many authors have found solution of this complex problem by using Adomain Decomposition Method (ADM), Reduced Differential Transform Method (RDTM) etc. All of these methods have a drawback as their convergence is quite slow and it requires a very good approximation to converge these schemes in considerable iterations. To overcome this difficulty, Liao has proposedHomotopy Analysis Method (HAM) that is quite effective due to the presence of convergence control parameter ħ. It has been shown that for ħ = −0.7, the scheme converges after very few iterations. Analytical solution obtained by HAM has been compared with the exact solution and both are found in good agreement. Computations are performed using the software package MATHEMATICA.This work verifies the validity and the potential of the HAM for the study of nonlinear systems of partial differential equations.