Operator-Difference Schemes for Systems of First-Order Integro-Differential Equations

Abstract

We consider the Cauchy problem for a system of two first-order integro-differentialequations with memory in finite-dimensional Hilbert spaces, where the integral term contains adifference kernel. Such a mathematical model is typical for nonstationary electromagneticprocesses taking into account the electric field dispersion effects. To obtain an approximatesolution of the considered nonlocal problem, a transformation to a local Cauchy problem fora system of first-order equations is applied, based on approximating the difference kernel by a sumof exponentials. Two-level operator-difference schemes in Hilbert spaces are constructed andanalyzed for stability.