Stable and Conservative Finite Difference Time-Domain Methods for Rotating Nonlinear Klein-Gordon Equation
Year: 2025
Author: Tingchun Wang, Tingfeng Wang, Xiaofei Zhao
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 615–649
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2024-051.010824
East Asian Journal on Applied Mathematics, Vol. 15 (2025), Iss. 3 : pp. 615–649
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Rotating nonlinear Klein-Gordon/wave equation angular momentum operator cosmic superfluid finite difference stability conservative schemes.