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Volume 22, Issue 2
Energy-Conservative Finite Difference Method for the Coupled Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime

Ming Cui & Yanfei Li

DOI: 10.4208/ijnam2025-1012

Int. J. Numer. Anal. Mod., 22 (2025), pp. 246-267.

Published online: 2025-02

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  • 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 $ε.$

  • Keywords

Coupled nonlinear Klein-Gordon equations, finite difference time domain method, energy-conservative, cut-off technique, nonrelativistic regime.

  • AMS Subject Headings

65N06, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-22-246, author = {Cui , Ming and Li , Yanfei}, title = {Energy-Conservative Finite Difference Method for the Coupled Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {2}, pages = {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 $ε.$

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1012}, url = {http://global-sci.org/intro/article_detail/ijnam/23823.html} }
TY - JOUR T1 - Energy-Conservative Finite Difference Method for the Coupled Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime AU - Cui , Ming AU - Li , Yanfei JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 246 EP - 267 PY - 2025 DA - 2025/02 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1012 UR - https://global-sci.org/intro/article_detail/ijnam/23823.html KW - Coupled nonlinear Klein-Gordon equations, finite difference time domain method, energy-conservative, cut-off technique, nonrelativistic regime. AB -

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 $ε.$

Cui , Ming and Li , Yanfei. (2025). Energy-Conservative Finite Difference Method for the Coupled Nonlinear Klein-Gordon Equation in the Nonrelativistic Limit Regime. International Journal of Numerical Analysis and Modeling. 22 (2). 246-267. doi:10.4208/ijnam2025-1012
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