IMPLICIT DIFFERENCE METHODS FOR PARABOLIC FDE ON CYLINDRICAL DOMAINS

Implicit difference schemes for quasilinear parabolic functional differential equations are presented. Ben- efits of implicit methods are pointed. The attention is focused here on cylindrical domains. Operators approximating mixed derivatives on irregular grids are introduced. A complete convergence analysis for methods is presented. Nonlinear estimates of the Perron type for given functions with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables. Numerical examples display the results of our investigations.