An efficient iterative scheme for the analytical-numerical solution of multi-dimensional nonlinear Burgers' equations

This article proposes a simple yet efficient/powerful iterative scheme to obtain approximate solutions to a class of nonlinear parabolic partial differential equations. The approximation method is based on the residual error function and the multiple power series expansion. Error estimates are derived and convergence of the proposed method is established. Several numerical examples are then considered to validate the theoretical results and highlight the computational ease of the developed residual power series method on multi-dimensional nonlinear Burgers’ equations. It is observed that the proposed approximation method captures shock wave propagation and steep gradient formation very well, and delivers more accurate results than the contemporary methods in higher dimensions.