A Comparison Of Adomian Decomposition Method And Variational Iteration Method For Solving Burger?�?s Fisher Equation

Abstract

This study provides a comparative study of the Adomian Decomposition Method and the He’s Variational iteration method to obtain analytic approximations of nonlinear space time Burger’s fisher equation that arises in a modeling of gas dynamics, financial mathematics, sound waves in a viscous medium etc. ADM and VIM are applied for solving Burger’s fisher equation, which is a nonlinear second order partial differential equation involving the first derivative in time. Adomian decomposition method (ADM) needs Adomian polynomial formula. But He’s variational iteration method (VIM) needs determining the general Lagrange Multiplier, which is optimal value.Moreover, two test examples were solved both by ADM and VIM based on the analysis obtained and their convergence and accuracy has been seen. Approximate analytic solutions calculated by ADM and Variational iteration method (VIM) are compared with the exact solutions for different values of x and t in order to obtain the absolute errors. The maximum absolute errors have been seen in ADM than VIM and it has been proved that VIM has a good convergence and accuracy than ADM in solving Burger’s fisher equation. Finally, the results are presented graphically.