摘要
以一维非线性Maxwell方程为模型,针对非一致介质时交界处弱间断和间断两种情况,研究了多区域Legendre tau方法.时间离散采用leapfrog-Crank-Nicolson三层格式,显隐结合提高了算法的稳定性和求解效率;证明了格式的稳定性,并获得按最优阶L2-误差估计.数值算例验证了多区域Legendre tau方法对于该非线性间断问题的有效性.
Taking the 1-D nonlinear Maxwell’s equation as a model,the multidomain Legendre tau method is studied for the cases of weak discontinuity and discontinuity at the interface of nonhomogeneous media.The leapfrog-Crank-Nicolson scheme is used for time discretization,which is a three-level explicit-implicit method of good stability and easy implementation.The stability of the scheme is proved,and the L2-error estimate of optimal order is obtained.Numerical examples show the effectiveness of the proposed multidomain Legendre tau method for such nonlinear discontinuous problems.
作者
姚佳倩
马和平
YAO Jiaqian;MA Heping(College of Sciences,Shanghai University,Shanghai 200444,China)
出处
《上海大学学报(自然科学版)》
北大核心
2025年第6期1087-1102,共16页
Journal of Shanghai University:Natural Science Edition
基金
国家自然科学基金资助项目(11971016)。
