Compact difference schemes for Klein–Gordon equation with variable coefficients
https://doi.org/10.29235/1561-8323-2021-65-1-25-32
Abstract
In this paper, we consider the compact difference approximation of the fourth and second-order schemes on a three-point stencil for Klein–Gordon equations with variable coefficients. Despite the linearity of the differential and difference problems, it is not possible in this case to apply the well-known results on the theory of stability of three-layer operator-difference schemes by A. A. Samarskii. The main purpose is to prove the stability with respect to the initial data and the right-hand side of compact difference schemes in the grid norms L2(Wh), W12 (Wh), C (Wh). Using the method of energy inequalities, the corresponding a priori estimates, expressing the stability and convergence of the solution to the difference problem with the assumption h ≤ = h0, h0 = const, τ≥h is obtained. The conducted numerical experiment shows how Runge rule is used to determine the different orders of the convergence rate of the difference scheme in the case of two independent variables.
About the Authors
P. P. Matus
Institute of Mathematics of the National Academy of Sciences of Belarus; Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin
Belarus
Belarus
Matus Piotr P. – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief researcher
11, Surganov Str., 220072, Minsk
H.T.K. Anh
Belarusian State University
Belarus
Belarus
Hoang Thi Kieu Anh – Postgraduate student
4, Nezavisimosti Ave., 220030, Minsk
References
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