Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels

We consider the problems of numerical solution Cauchy problem for an evolutionary equation with memory when kernel integral term is a difference one. The computational implementation associated need to work approximate all previous points in time. In this paper, considered nonlocal transformed into local one; loosely coupled system additional ordinary differential equations solved. This approach based on approximation by sum exponentials. Estimates stability concerning initial data and right-hand side corresponding are obtained. Two-level schemes weights convenient constructed investigated. theoretical consideration supplemented results integrodifferential stretching exponential function.