Numerical Solution Of Burger-Fisher Equation Using Variational Iteration Method (Vim)

Abstract

The Burger-Fisher equations occur in various areas of applied sciences and physical applications, such as modeling of gas dynamics, financial Mathematics and fluid mechanics. This equation (BFE) is a non-linear partial differential equation. In this thesis the variational iteration method (VIM) has been used to obtain the solutions of Burger Fisher Equations (BFE). This method (VIM) is based on General Lagrange multiplier, restricted variation and correction functional which are the main concepts of VIM. Using this method creates a sequence which tends to the exact solution of the problem. The advantage of VIM so that, it does not require linearization, a small parameter and Adomian polynomial in an equation as perturbation technique needs. The VIM is used to solve effectively, and easily a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, its exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. Two numerical examples present in this thesis by using tables and graphs suggest that this method is a powerful series approach to find numerical solutions that are in good agreement with the exact solution.