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Estimate of solutions for differential and difference functional equations with applications to difference methods. (English) Zbl 1221.65224

Theorems on the estimate of solutions for nonlinear second-order partial differential functional equations mainly of parabolic type with Dirichlet condition and for suitable explicit finite difference functional schemes are presented. The convergent difference method given is considered without an assumption of the global generalized Perron condition on the functional variable.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35R10 Partial functional-differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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