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A Three‐Level Time‐Split MacCormack Method for Two‐Dimensional Nonlinear Reaction‐Diffusion Equations
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-05-04 , DOI: 10.1002/fld.4844 Eric Ngondiep 1, 2 , Nabil Kerdid 1 , Mohammed Abdulaziz Mohammed Abaoud 1 , Ibrahim Abdulaziz Ibrahim Aldayel 1
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-05-04 , DOI: 10.1002/fld.4844 Eric Ngondiep 1, 2 , Nabil Kerdid 1 , Mohammed Abdulaziz Mohammed Abaoud 1 , Ibrahim Abdulaziz Ibrahim Aldayel 1
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A three-level explicit time-split MacCormack scheme is proposed for solving the two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced thank to the splitting and the explicit MacCormack scheme. Under the well known condition of Courant-Friedrich-Lewy (CFL) for stability of explicit numerical schemes applied to linear parabolic partial differential equations, we prove the stability and convergence of the method in $L^{\infty}(0,T;L^{2})$-norm. A wide set of numerical evidences which provide the convergence rate of the new algorithm are presented and critically discussed.
中文翻译：
二维非线性反应扩散方程的三级时分 MacCormack 方法
提出了一种用于求解二维非线性反应扩散方程的三级显式时间分割MacCormack方案。由于拆分和显式 MacCormack 方案，计算成本降低。在众所周知的 Courant-Friedrich-Lewy (CFL) 条件下，显式数值格式应用于线性抛物线偏微分方程的稳定性，我们证明了该方法在 $L^{\infty}(0,T; L^{2})$-范数。提出并批判性地讨论了提供新算法收敛速度的大量数值证据。
更新日期：2020-05-04
中文翻译：
二维非线性反应扩散方程的三级时分 MacCormack 方法
提出了一种用于求解二维非线性反应扩散方程的三级显式时间分割MacCormack方案。由于拆分和显式 MacCormack 方案，计算成本降低。在众所周知的 Courant-Friedrich-Lewy (CFL) 条件下，显式数值格式应用于线性抛物线偏微分方程的稳定性，我们证明了该方法在 $L^{\infty}(0,T; L^{2})$-范数。提出并批判性地讨论了提供新算法收敛速度的大量数值证据。
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