Compact difference schemes for multidimensional Klein–Gordon equations
https://doi.org/10.29235/1561-8323-2022-66-1-12-20
Abstract
Abstract. In this article, we consider a compact difference approximation of the schemes of order O(| h|4 + τ2), h = (h1, h2, ..., hp) for the Klein–Gordon equations in the multidimensional case. In studying the stability of these difference schemes, the theory of operator-difference schemes by A. A. Samarskii is used, and the strong stability of difference schemes is proved with respect to a small perturbation of the initial conditions, the right-hand side and the coefficients of the equations. The theoretical results are confirmed by test numerical calculations.
Keywords
compact difference schemes,
multidimentional Klein–Gordon equation,
priori estimates,
stability,
convergence
Supporting agencies: The author expresses her sincere gratitude to Professor P.P. Matus for help, advice and recommendations received during the preparation of this work
About the Author
Thi Kieu Anh Hoang
Belarusian State University; Ho Chi Minh City University of Natural Resources and Environment
Viet Nam
Viet Nam
Hoang Thi Kieu Anh – Postgraduate student.
4, Nezavisimosti Ave., 220030, Minsk
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