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Implicit difference methods for nonlinear parabolic functional differential systems

Kropielnicka K.

Demonstratio Mathematica

2006

Vol. 39, nr 3

711-728

Classical solutions of initial boundary value problems are approximated in the paper by solutions of implicit difference schemes. A convergence analysis for methods is presented. It is shown by an example that the new methods are considerably better than the explicit schemes. The proof of the stability is based on a theorem on difference inequalities. Nonlinear estimates of the Perron type for given functions with respect to functional variables are used. The results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.