An efficient semi-analytical technique to solve multi-dimensional Burgers’ equation

Abstract

The work of this paper is motivated by the recently published article (Zeidan et al., Math Methods Appl Sci 43(5):2171–2188, 2020) in which the authors have discussed the Adomian decomposition method (ADM) to solve one dimensional Burgers’ equation in viscous and inviscid forms. Here, we propose an effective and efficient semi-analytical method named variational iteration method (VIM) (He, Int J Non-linear Mech 34(4):699–708, 1999) to solve the Burgers’ equations considered in Zeidan et al. (Math Methods Appl Sci 43(5):2171–2188, 2020). The novelty of the proposed scheme over ADM is proven by comparing the truncated series solutions and presented in the form of graphs and error tables. In addition to this, VIM is extended to solve 2D, 3D, and systems of Burgers’ equations. Thanks to the scheme, closed-form solutions are obtained in most of the cases. The convergence analysis is also investigated for all the test problems.