Optimal error estimates of fourth-order compact finite difference methods for the nonlinear Klein-Gordon equation in the nonrelativistic regime

被引：6
|
作者：
Zhang, Teng [1 ]
Wang, Tingchun [2 ]
机构：
[1] Natl Univ Singapore, Dept Math, Singapore, Singapore
[2] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 37卷 / 03期
基金：
中国国家自然科学基金;
关键词：
compact finite difference method; Klein– Gordon equation in the nonrelativistic regime; optimal error estimate; PSEUDOSPECTRAL METHOD; NUMERICAL-SOLUTION; CAUCHY-PROBLEM; LIMIT; SCHEMES; INTEGRATORS;
D O I：
10.1002/num.22664
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Two fourth-order compact finite difference schemes including a Crank-Nicolson one and a semi-implicit one are derived for solving the nonlinear Klein-Gordon equations in the nonrelativistic regime. The optimal error estimates and the strategy in choosing time step are rigorously analyzed, and the energy conservation in the discrete sense is also studied. Under proper assumption on the analytical solutions, the errors of the two schemes both are proved to be of O(h(4)+tau(2)/epsilon(6)) with mesh size h and time-step tau. Numerical simulations are provided to confirm the theoretical analysis.
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页码：2089 / 2108
页数：20
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