Implicit difference methods for nonlinear first order partial functional differential systems

Volume 37 / 2010

Elżbieta Puźniakowska-Gałuch Applicationes Mathematicae 37 (2010), 459-482 MSC: 35F25, 41A65, 65Q10. DOI: 10.4064/am37-4-5


Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type. Numerical examples are given.


  • Elżbieta Puźniakowska-GałuchInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz St. 57
    80-952 Gdańsk, Poland

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