Exact Solution of 3-Dimensional Burgers Equation Using Homotopy Perturbation Method-Sumudu Transform

Abstract

This article discusses the solution of the Burgers equation, which is a nonlinear partial differential equation, particularly for the 3D Burgers equation. This equation will be solved using a combination of the Homotopy Perturbation Method (HPM) and the Sumudu Transform (ST), known as HPM-ST. HPM-ST an alternative method to those found in the existing literature. This method is effective and easy to determine the analytic solution of nonlinear equations. To implement HPM-ST, the Sumudu transform and inverse Sumudu transform are applied first, so a nonlinear differential equation is obtained that does not depend on the variable t. Then, HPM is applied to this equation to derive an infinite series, which can be approximated using a Maclaurin series. The analytical solution of the 3D Burgers equation obtained by HPM-ST is equivalent to the exact solution. To provide an overview of the solution of the 3D Burgers equation, a visualization of the obtained solution is also presented using MATLAB.