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 - <p style="text-align: justify;">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 $0 &lt; ε ≪ 1$ 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 $ε.$</p>