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Mathematical studies of the solution of Burgers' equations by Adomian decomposition method
Author(s) -
Zeidan Dia,
Chau Chi Kin,
Lu TzonTzer,
Zheng WeiQuan
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5982
Subject(s) - adomian decomposition method , mathematics , exact solutions in general relativity , burgers' equation , inviscid flow , partial differential equation , decomposition method (queueing theory) , decomposition , differential equation , mathematical analysis , classical mechanics , ecology , physics , discrete mathematics , biology
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.