 A class of compact finite difference schemes for solving the 2D and 3D Burgers’ equationsXiaojia Yang, Yongbin Ge and Bin Lan Mathematics and Computers in Simulation (MATCOM), 2021, vol. 185, issue C, 510-534 Abstract: In this paper, a class of two-level high-order compact finite difference implicit schemes are proposed for solving the Burgers’ equations. Firstly, based on the fourth-order compact finite difference schemes for spatial derivatives and the truncation error remainder correction method for temporal derivative, the high-order compact (HOC) difference method is introduced for solving the one-dimensional (1D) Burgers’ equation. At the same time, the stability of the scheme is analyzed by using the Fourier analysis method. Because only three grid points are involved in each time level. The Thomas algorithm can be directly used to solve the tridiagonal linear system. Then, this method is extended to solve the two-dimensional (2D) and three-dimensional (3D) coupled Burgers’ equations. Finally, numerical experiments are conducted to verify the accuracy and the reliability of the present schemes. Keywords: Burgers’ equation; Compact difference scheme; Implicit scheme; High accuracy; Stability analysis (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:185:y:2021:i:c:p:510-534 DOI: 10.1016/j.matcom.2021.01.009 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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