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Compact Difference Schemes for the Multidimensional Klein–Gordon Equation

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Abstract

Stable compact difference schemes of \(4+2\) and \(4+4 \) approximation orders are considered and studied on standard stencils for the multidimensional Klein–Gordon equation with both constant and variable coefficients. The results obtained are generalized to initial–boundary value problems for second-order quasilinear equations of hyperbolic type. It is proved that compact difference schemes of increased order of approximation can be reduced to three-level schemes with constant or variable weights, which permits one to use the previously developed theory of stability of operator-difference schemes with operators acting in finite-dimensional Euclidean spaces for their analysis. A priori estimates for the stability and convergence of the difference solution in mesh analogs of Sobolev spaces are obtained. The results of computational experiments are presented.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, 220072, Belarus

    P. P. Matus

  2. The John Paul Catholic University of Lublin, Lublin, 20-950, Poland

    P. P. Matus

  3. Belarusian State University, Minsk, 220030, Belarus

    Hoang Thi Kieu Anh

  4. University of Natural Resources and Environment, Ho Chi Minh, Viet Nam

    Hoang Thi Kieu Anh

Authors
  1. P. P. Matus
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  2. Hoang Thi Kieu Anh
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Correspondence to P. P. Matus or Hoang Thi Kieu Anh.

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Translated by V. Potapchouck

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Matus, P.P., Hoang Thi Kieu Anh Compact Difference Schemes for the Multidimensional Klein–Gordon Equation. Diff Equat 58, 120–138 (2022). https://doi.org/10.1134/S0012266122010128

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  • DOI: https://doi.org/10.1134/S0012266122010128

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