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Browsing by Subject "interpolating operators"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Difference functional inequalities and applications
    (2014) Szafrańska, Anna
    The paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Numerical approximations of difference functional equations and applications
    (2005) Kamont, Zdzisław
    We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.