Finite-difference approximation of first-order partial differential-functional equations - Kamont, Z. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We consider initial boundary-value problems of Dirichlet type for nonlinear equations. We give sufficient conditions for the convergence of a general class of one-step difference methods. We assume that the right-hand side of the equation satisfies an estimate of Perron type with respect to the functional argument.