TY - JOUR
T1 - Stable and Conservative Finite Difference Time-Domain Methods for Rotating Nonlinear Klein-Gordon Equation
AU - Wang , Tingchun
AU - Wang , Tingfeng
AU - Zhao , Xiaofei
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 615
EP - 649
PY - 2025
DA - 2025/06
SN - 15
DO - http://doi.org/10.4208/eajam.2024-051.010824
UR - https://global-sci.org/intro/article_detail/eajam/24158.html
KW - Rotating nonlinear Klein-Gordon/wave equation, angular momentum operator, cosmic superfluid, finite difference, stability, conservative schemes.
AB - <p style="text-align: justify;">We consider numerical discretizations for nonlinear Klein-Gordon/wave equations in a rotating frame. Due to the strong centrifugal forces in the model, non-proper
spatial discretizations of the rotating terms (under finite difference or finite element)
would lead to numerical instability that cannot be overcome by standard time averages.
We identify a class of boundary-stable type finite difference discretizations. Based on
it, we propose several stable and accurate finite difference time-domain schemes with
discrete conservation laws. Extensive numerical experiments and simulations are done
to understand the significance of the model and the proposed schemes.</p>