The paper deals with the local Cauchy problem for first order partial functional differential systems. A general class of difference methods is constructed. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that the given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential systems with deviated variables and differential integral problems can be obtained from a general case by specializing the given operators. The results are illustrated by numerical examples.
"Difference methods for quasilinear hyperbolic differential functional systems on the Haar pyramid." Bull. Belg. Math. Soc. Simon Stevin 10 (2) 267 - 290, June 2003. https://doi.org/10.36045/bbms/1054818028