Energy-Conservative Finite Difference Method for the Coupled Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime
Year: 2025
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 246–267
Abstract
In this paper, we propose an energy-conservative finite difference time domain (FDTD) method for solving the coupled nonlinear Klein-Gordon equations (CNKGEs) in the nonrelativistic limit regime, involving a small parameter $0 < ε ≪ 1$ which is inversely proportional to the speed of light. Employing cut-off technique, we analyze rigorously error estimates for the numerical method. Numerical results are reported to confirm the energy-conservative property and the error results in $l^2$ norm and $H^1$ norm under different values of $ε.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1012
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 246–267
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Coupled nonlinear Klein-Gordon equations finite difference time domain method energy-conservative cut-off technique nonrelativistic regime.