DIFFERENCE-METHODS FOR IMPULSIVE DIFFERENTIAL-FUNCTIONAL EQUATIONS

We consider a class of difference methods for initial value problems f or first-order impulsive partial differential-functional equations. We give sufficient conditions for the convergence of a sequence of appro ximate solutions under the assumptions that the right-hand sides satis fy the nonlinear estimates of Perron type with respect to the function al argument. The proof of the stability of difference methods is based on a general theorem on the error estimate of approximate solutions f or difference-functional equations of Volterra type with an unknown fu nction of several variables.