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Globally Stable Difference Schemes for the Fisher Equation

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Abstract

Unconditionally monotone and globally stable difference schemes for the Fisher equation are constructed and investigated. It is shown that for a certain choice of input data, these schemes inherit the main property of a stable solution of the differential problem. The unconditional monotonicity of the difference schemes under consideration is proved, and an a priori estimate for the difference solution in the uniform norm is obtained. The stable behavior of the difference solution in the nonlinear case is proved under strict constraints on the input data. The results obtained are generalized to multidimensional equations, for the approximation of which economical difference schemes are used.

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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 & D. Pylak

Authors
  1. P. P. Matus
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  2. D. Pylak
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Correspondence to P. P. Matus or D. Pylak.

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Translated by V. Potapchouck

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Matus, P.P., Pylak, D. Globally Stable Difference Schemes for the Fisher Equation. Diff Equat 59, 962–969 (2023). https://doi.org/10.1134/S0012266123070091

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  • DOI: https://doi.org/10.1134/S0012266123070091

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