OPERATOR-DIFFERENCE SCHEMES FOR SYSTEMS OF FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

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Abstract

The Cauchy problem is considered for a system of two first-order integro-differential equations with memory in finite-dimensional Hilbert spaces, where the integral term contains a difference kernel. Such mathematical model is typical for nonstationary electromagnetic processes, taking into account the dispersion effects of the electric field. To obtain an approximate solution to the considered nonlocal problem, a transformation to a local Cauchy problem for a system of first-order equations is applied, based on approximating the difference kernel by a sum of exponentials. Two-level operator-difference schemes in Hilbert spaces are constructed and analyzed for stability.

About the authors

P. N Vabishchevich

Lomonosov Moscow State University; North Caucasus Federal University

Email: vab@cs.msu.ru
Moscow, Russia; Stavropol, Russia

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