Variation Iteration Method for The Approximate Solution of Nonlinear Burgers Equation

Abstract

In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation was carried out on the Burgers equation with the Variational Iteration Method (VIM). The resulting solution showed that the rate of convergence decreases with increase in the values of the parameters x and t at each iterate level. However, as the number of iterations increases, there is a rapid rate of convergence of the approximate solution to the analytic solution. Results obtained with the Variational Iteration Method (VIM) on the Burgers equation were compared with the exact found in literature. All computational framework of the research were performed with the aid of Maple 18 software.

Keywords: Variational Iteration Method, Burgers Equation, Partial Differential Equations, Approximate Solution, Mean Value Theorem, Schwartz Inequality.