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Temporal convergence of extrapolated BDF-2 scheme for the Maxwell-Landau-Lifshitz equations
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2022-06-08 , DOI: 10.1016/j.camwa.2022.05.037
Shuaifei Hu, Guomei Zhao, Rong An

The Maxwell-Landau-Lifshitz equations are used to describe certain electromagnetic phenomena and are a strongly nonlinear parabolic system. This paper focuses on the optimal error estimates of a linearized second-order BDF semi-discrete scheme for the numerical approximation of the solution to the Maxwell-Landau-Lifshitz equations. The proposed algorithm is a semi-implicit scheme by using the extrapolation technique and the implicit-explicit method to linearize the nonlinear terms. Furthermore, the second-order temporal convergence rate O(τ2) is derived, where τ is the time step size. Finally, the numerical experiment is presented to confirm the theoretical result.



中文翻译:

Maxwell-Landau-Lifshitz 方程外推 BDF-2 格式的时间收敛

Maxwell-Landau-Lifshitz 方程用于描述某些电磁现象,是一个强非线性抛物线系统。本文重点研究了 Maxwell-Landau-Lifshitz 方程解的数值逼近的线性化二阶 BDF 半离散格式的最优误差估计。该算法是一种半隐式方案,使用外推技术和隐式-显式方法对非线性项进行线性化。此外,二阶时间收敛速度(τ2)推导出来,其中τ是时间步长。最后通过数值实验验证了理论结果。

更新日期:2022-06-09
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