Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

By Dia Zeidan, C. Chau, Tzon-Tzer Lu, Weimin Zheng. Mathematical methods in the applied sciences, 2019

49 citations recorded by the source corpus.

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi‐analytic solution. In the best cases, when a closed‐form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1d1a6566c55829583da4c2282c7b490c7cf87965