Mathematical studies of the solution of Burgers' equations by Adomian decomposition method |
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Authors: | Dia Zeidan Chi Kin Chau Tzon-Tzer Lu Wei-Quan Zheng |
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Affiliation: | 1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan;2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, R.O.C |
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Abstract: | 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. |
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Keywords: | Adomian decomposition method analytical solution Burgers' equation closed-form solution semi-analytical solution |
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