Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime

JOURNAL OF COMPUTATIONAL PHYSICS

卷:398

Article

Bao, Weizhu¹  Zhao, Xiaofei² 

[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

关键词: Nonlinear Klein-Gordon equation;    Nonrelativistic limit regime;    Numerical schemes;    Comparison;    epsilon-resolution;    Uniformly accurate;   

DOI  :  10.1016/j.jcp.2019.108886

来源: Elsevier

【 摘 要 】

Different efficient and accurate numerical methods have recently been proposed and analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter epsilon is an element of (0, 1], which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. 0 < epsilon << 1, the solution of the NKGE propagates waves with wavelength at O(1) and O(epsilon(2)) in space and time, respectively, which brings significantly numerical burdens in designing numerical methods. We compare systematically spatial/temporal efficiency and accuracy as well as epsilon-resolution (or epsilon-scalability) of different numerical methods including finite difference time domain methods, time-splitting method, exponential wave integrator, limit integrator, multiscale time integrator, two-scale formulation method and iterative exponential integrator. Finally, we adopt the multiscale time integrator to study the convergence rates from the NKGE to its limiting models when e -> 0(+). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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