Abstract
We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional dierential equations. Dierence methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite dierence systems. Methods of second type are truncation of the infinite dierence system, so that the resulting dierence problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-dierenti al problems can be obtained from the general model by specifying the given operators.
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