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numerical analysis of a linear generalized finite difference scheme for Burgers' equation

Computers and Mathematics with Applications 2025年 193卷 117-131页

作者： Wang, Kai Li, Yubo Wu, Anping Yin, Xiaoxin Liu, Feng Feng, Xinlong College of Mathematics and Systems Science Xinjiang University Urumqi 830017 China Hypervelocity Aerodynamics Institute China Aerodynamics Research and Development Center Sichuan Province Mianyang 621010 China National Key Laboratory of Aerospace Physics in Fluids Sichuan Province Mianyang 621010 China School of Computer Science and Technology Southwest University of Science and Technology Sichuan Province Mianyang 621010 China

In this study, we solved the Burgers' equation using a generalized finite-difference method and constructed a two-layer explicit scheme. The Generalized Finite Difference Method (GFDM) is a meshless collocation method for solving partial differential equations. By using GFDM, it is possible to avoid constructing meshes for simulations. Moreover, due to the property of the moving least-square approximation in GFDM, the resulting matrix system can be formed into a sparse matrix, which makes GFDM suitable for solving large-scale problems. Subsequently, we performed a numerical analysis of the scheme. The maximum norm error estimate of the linear difference scheme was proven, demonstrating second-order convergence in both time and space with appropriate parameter selection. Finally, we verify our conclusions using five numerical examples. The numerical results were consistent with the theoretical analysis, comprehensively validating the excellent performance of the constructed two-layer explicit generalized finite-difference scheme for solving the Burgers' equation. © 2025 Elsevier Ltd

关键词： Burgers' equation Generalized Finite Difference Method linear meshless numerical scheme

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