ON THE APPROXIMATION OF A BOUNDARY VALUE PROBLEM FOR DELAY INTEGRO-DIFFERENTIAL EQUATIONS

A linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is investigated on a finite interval. By dividing the interval by parts, the integral term of the integrodifferential equation with constant delay argument is replaced by the quadrature formula. With this replacement, the linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is approximated by the linear boundary value problem for a system of loaded differential equations with a constant delay argument. Definitions of correct solvability of boundary value problem for system of integro-differential equations with delay argument and constructed boundary value problem for system of loaded differential equations with constant delay argument are introduced. Conditions of correct solvability of linear boundary value problem for system of integro-differential equations with delay argument and linear boundary value problem for system of loaded differential equations with delay argument are established. Relationship between correct solvabilities of linear two-point boundary value problem for system of integro-differential equations with constant delay argument and approximating linear two-point boundary value problem for system of loaded differential equations with constant delay argument is shown.

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