Comparison of explicit and implicit difference methods for quasilinear functional differential equations

Tom 38 / 2011

W. Czernous, Z. Kamont Applicationes Mathematicae 38 (2011), 315-340 MSC: 65M12, 35R10. DOI: 10.4064/am38-3-4

Streszczenie

We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit and implicit difference methods.

We use a comparison technique with nonlinear estimates of Perron type for given functions with respect to the functional variables.

Autorzy

  • W. CzernousInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz St. 57
    80-952 Gdańsk, Poland
    e-mail
  • Z. KamontInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz St. 57
    80-952 Gdańsk, Poland
    e-mail

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