 Optimized decomposition method for solving multi-dimensional Burgers’ equationSonali Kaushik and Rajesh Kumar Mathematics and Computers in Simulation (MATCOM), 2023, vol. 208, issue C, 326-350 Abstract: The objectives of this article are to deal with computing the series solutions of 1D dimensionless Burgers’ equation using the optimized decomposition method (ODM) and the extension of ODM to the system of PDEs which aids in dealing with multi-dimensional Burgers’ equation. Several examples of the inviscid and viscous 1D Burgers’ equations are considered to demonstrate the implementation of the scheme. In this case, it is shown that ODM provides better estimates than the existing Adomian decomposition method (ADM). Owing to the advantage of ODM over ADM, the extension of ODM is used to calculate the semi-analytical approximate solutions of the dimensionless 2D and 3D Burgers’ equations. In most cases, it is observed that the series solution gives the closed-form solution. Moreover, in all the examples, the finite term approximate solutions obtained by the proposed method are shown to provide good accuracy with the exact solutions. The theoretical convergence results are also established to showcase the efficacy of our technique. Keywords: Inviscid Burgers’ equation; Viscous Burgers’ equation; ODM; ADM; Semi-analytical approximations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:208:y:2023:i:c:p:326-350 DOI: 10.1016/j.matcom.2023.01.043 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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