LOCAL COMPUTATIONAL ALGORITHMS FOR THE SYSTEM OF FIRST-ORDER EQUATIONS WITH MEMORY EFFECTS

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Аннотация

We consider the Cauchy problem for a system of integro-differential equations of the first order with difference kernels in finite-dimensional Hilbert spaces. This class of equations arises in the mathematical modeling of a wide range of nonstationary processes taking into account memory effects, including, in particular, the system of Maxwell's equations. For numerical solution, a method of reducing the original nonlocal problem to an equivalent system of local differential equations of the first order on the basis of approximation of kernels by a finite sum of exponential functions is proposed. Two-level operator-difference schemes are proposed, for which the stability of the initial data and the right-hand side is analyzed. The performed theoretical analysis demonstrates the correctness of the proposed approach.

Авторлар туралы

A. Alikhanov

North Caucasus Federal University

Email: aalikhanov@ncfu.ru
Stavropol, Russia

P. Vabishchevich

Lomonosov Moscow State University

Email: vab@cs.msu.ru
Russia

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