Solution of Non-Linear Ito System of Equations by Homotopy Analysis Method (HAM)
Keywords:
Ito coupled system, Adomian decomposition method,homotopy analysis method, analytical solutions, symbolic computation, Mathematica.Abstract
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.
Mathematics Subject Classification:58B05, 55U40, 34A34, 35C10, 34A45.