Solving the System of Two-Dimensional Coupled Burgers' Equations byModified Variational Iteration Method with Genetic Algorithm

Abstract

In this paper, a new modified variational iteration method (MVIM) with a genetic algorithm has been applied for solving nonlinear partial differential equations. Therefore, a new correction function through an auxiliary parameter  that makes sure the convergence of the standard method and improved results by using genetic techniques are introduced. The standard variational iteration method (VIM) is first applied to solve numerically the system of two-dimensional coupled Burgers' equations. Then an improvement on this method is done. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of this method. The algorithm converges readily which yields correct solutions. Better accuracy in comparison with other previous methods has been noticed. Moreover, the method can be easily applied to a wide number of linear and nonlinear differential equations with better accuracy.