Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Volume 103 / 2012

Zdzisław Kamont, Karolina Kropielnicka Annales Polonici Mathematici 103 (2012), 135-160 MSC: Primary 35R10; Secondary 65M12. DOI: 10.4064/ap103-2-3

Abstract

Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It is shown that the conditions on the mesh for explicit difference schemes are more restrictive than the suitable assumptions for implicit methods. There are implicit difference schemes which are convergent while the corresponding explicit difference methods are not convergent. Error estimates for both methods are constructed.

Authors

  • Zdzisław KamontInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz Street 57
    80-952 Gdańsk, Poland
    e-mail
  • Karolina KropielnickaInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz Street 57
    80-952 Gdańsk, Poland
    e-mail

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