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Implicit difference methods for parabolic functional differential equations
Author(s) -
Czernous W.,
Kamont Z.
Publication year - 2005
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200410186
Subject(s) - mathematics , nonlinear system , convergence (economics) , variable (mathematics) , stability (learning theory) , mathematical analysis , differential equation , class (philosophy) , type (biology) , computer science , ecology , physics , quantum mechanics , machine learning , artificial intelligence , biology , economic growth , economics
We present a new class of numerical methods for the solution of quasilinear parabolic functional differential equations. The numerical methods are difference schemes which are implicit with respect to time variable. We give a complete convergence analysis for the methods and we show by an example that the new methods are considerable better that the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. Results obtained in the paper can be applied to differential integral problems and equations with retarded variables.