### On inequalities between solutions of first order partial differential-functional equations

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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both methods. It...

Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.

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