Difference methods for parabolic functional differential problems of the Neumann type

Volume 92 / 2007

K. Kropielnicka Annales Polonici Mathematici 92 (2007), 163-178 MSC: 65M12, 35R10. DOI: 10.4064/ap92-2-5


Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given functions are used. Numerical examples are given.


  • K. KropielnickaInstitute of Mathematics
    University of Gdańsk
    57, Wit Stwosz St.
    80-952 Gdańsk, Poland

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