AbstractA general class of implicit difference methods for nonlinear parabolic
functional differential equations with initial boundary conditions of the Neumann type
is constructed. Convergence results are proved by means of consistency and stability
arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type
with respect to functional variables. Differential equations with deviated variables and
differential integral problems can be obtained from a general model by specializing
given operators. The results are illustrated by numerical examples.