期刊
MATHEMATICS AND COMPUTERS IN SIMULATION
卷 192, 期 -, 页码 265-277出版社
ELSEVIER
DOI: 10.1016/j.matcom.2021.09.002
关键词
Space-fractional Klein-Gordon equation; Fully-discrete energy-preserving scheme; Scalar auxiliary variable approach; Lagrange multiplier; Fourier pseudo-spectral method
类别
资金
- National Natural Science Foundation of China [12001210, 11701110]
- China Postdoctoral Science Foundation [2019M662946, 2020M682746]
- Hebei University Scientific Research Foundation, China for Higher-level Talents [521100221019]
- Ningxia Key Research and Development Program (Introduction of Talents Project) [2020BEB04039]
- Guangdong Basic and Applied Basic Research Foundation, China [2020B1515310005]
- Key Program of Guangxi Normal University [2016ZD001]
This paper develops a family of effective fully-discrete energy-preserving schemes for the space-fractional Klein-Gordon equation, utilizing special approximations and Fourier pseudo-spectral method. The method shows high efficiency and accuracy in numerical experiments.
A family of effective fully-discrete energy-preserving schemes for the space-fractional Klein-Gordon equation is developed in this paper. First, the recently developed Lagrange multiplier type scalar auxiliary variable approach is employed to obtain a new equivalent system from the original space-fractional Klein-Gordon system. Then, a family of special second-order implicit, explicit and implicit approximations to respectively discretize the linear parts, nonlinear parts and time-derivative parts are obtained in the above equivalent system to establish a family of semi-discrete (continuous in space) energy-preserving schemes. Furthermore, the Fourier pseudo-spectral method is used to discretize the space for extending to the fully-discrete case and rigorous theoretical proofs guarantee its conservation of original energy. Especially, the well-known implicit-explicit Crank-Nicolson type scheme is only one of the above-mentioned schemes. It is inspiring that the main computational efforts of this method in each time step are only to solve two linear, decoupled differential equations with constant coefficients different from non-homogeneous terms, which thus can be effectively solved. Finally, numerical experiments are carried out to verify the theoretical results of the accuracy, efficiency and conservation of original energy. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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