Numerical Solution of the Burgers’ Equation Using Chelyshkov Polynomials

Arar, Nouria; Deghdough, Bouchra; Dekkiche, Souad; Torch, Zineb; Nagy, A. M.

doi:10.1007/s40819-023-01663-8

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…Much effort has been dedicated to designing accurate and stable computing schemes to solve Burger's equation for large Reynolds numbers. According to the manner for spacial discretization, these schemes can be roughly categorized into mesh-based approaches [2][3][4][5][6][7][8] and mesh-free methods [9,10]. However, mesh-based approaches, such as finite difference/volume/element methods, seriously rely on deliberated meshes to discretize problem domain onto grid lines or elements to acquire accurate spacial approximation.…”

Section: Introductionmentioning

confidence: 99%

Explicit Numerical Manifold Characteristic Galerkin Method for Solving Burgers’ Equation

Sun,

Chen,

Chen

et al. 2024

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This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers’ equation. Employing the characteristic Galerkin method, we initially apply the Crank–Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully explicit form. For spacial discretization, we construct the NMM dual-cover system tailored to Burgers’ equation. We choose constant cover functions and first-order weight functions to enhance computational efficiency and exactly import boundary constraints. Finally, the integrated computing scheme is derived by using the standard Galerkin method, along with a Thomas algorithm-based solution procedure. The proposed method is verified through six benchmark numerical examples under various initial boundary conditions. Extensive comparisons with analytical solutions and results from alternative methods are conducted, demonstrating the accuracy and stability of our approach, particularly in solving Burgers’ equation at high Reynolds numbers.

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