Optimized decomposition method for solving multi-dimensional Burgers’ equation

Abstract

The objectives of this article are to deal with computing the series solutions of 1D dimensionless Burgers’ equation using the optimized decomposition method (ODM) and the extension of ODM to the system of PDEs which aids in dealing with multi-dimensional Burgers’ equation. Several examples of the inviscid and viscous 1D Burgers’ equations are considered to demonstrate the implementation of the scheme. In this case, it is shown that ODM provides better estimates than the existing Adomian decomposition method (ADM). Owing to the advantage of ODM over ADM, the extension of ODM is used to calculate the semi-analytical approximate solutions of the dimensionless 2D and 3D Burgers’ equations. In most cases, it is observed that the series solution gives the closed-form solution. Moreover, in all the examples, the finite term approximate solutions obtained by the proposed method are shown to provide good accuracy with the exact solutions. The theoretical convergence results are also established to showcase the efficacy of our technique