NUMERICALLY APPROXIMATE METHOD FOR SOLVING OF A CONTROL PROBLEM FOR INTEGRO-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE
Ключевые слова:partial integro-differential equations of parabolic type, problem with parameter, approximation, numericallyapproximate method, algorithm.
A linear boundary value problem with a parameter for integro-differential equations of parabolic type
is investigated. Using the spatial variable discretization, the considering problem is approximated by a linear
boundary value problem with a parameter for a system of ordinary integro-differential equations.The
parameterization method is used for solving the obtained problem. The approximating problem is reduced to an
equivalent problem consisting of a special Cauchy problem for the system of Fredholm integro-differential
equations, boundary conditions, and continuity conditions of the solution at the partition points. The solution of the
Cauchy problem for the system of ordinary differential equations with parameters is constructed using the
fundamental matrix of the differential equation. The system of a linear algebraic equations with respect to the
parameters are composed by substituting the values of the corresponding points in the boundary condition and the
continuity conditions. Numerical method for solving of the problem is suggested, which based on the solving of the
constructed system and method of Runge-Kutta 4-th order for solving of the Cauchy problem on the subintervals.