An economical robust algorithm for solving 1D coupled Burgers’ equations in a semi-Lagrangian framework
作者：
Highlights：
• Construction of a robust algorithm of an iteration method to resolve the nonlinearity of a system of coupled nonlinear reactiondiffusion equations.
• Proposing a new efficient method for finding the upstream points to reduce the computational cost without damaging the accuracy.
• Providing a heuristic error analysis of the proposed method.
• Numerically dealing with two new test cases of model problems (Examples 2 and 3).
• Showing that the proposed HUPA works well without non-physical oscillations with a relatively large time step size compared to the existing methods.
摘要
•Construction of a robust algorithm of an iteration method to resolve the nonlinearity of a system of coupled nonlinear reactiondiffusion equations.•Proposing a new efficient method for finding the upstream points to reduce the computational cost without damaging the accuracy.•Providing a heuristic error analysis of the proposed method.•Numerically dealing with two new test cases of model problems (Examples 2 and 3).•Showing that the proposed HUPA works well without non-physical oscillations with a relatively large time step size compared to the existing methods.
论文关键词：Backward semi-Lagrangian method,Error correction method,Coupled Burgers’ equations,Nonlinear Cauchy problem
论文评审过程：Received 17 July 2021, Revised 19 March 2022, Accepted 14 April 2022, Available online 3 May 2022, Version of Record 3 May 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127185
