East Asian J. Appl. Math., 15 (2025), pp. 615-649.
Published online: 2025-06
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2024-051.010824}, url = {http://global-sci.org/intro/article_detail/eajam/24158.html} }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.