Abstract
Classical solutions of mixed problems for first order partial functional differential systems in several independent variables are approximated in the paper with solutions of a difference problem of the Euler type. The mesh for the approximate solutions is obtained by a numerical solving of equations of characteristics. The convergence of explicit difference schemes is proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of the Perron type. Differential systems with deviated variables and differential integral systems can be obtained from a general model by specializing given operators.
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