NUMERICALLY APPROXIMATE METHOD FOR SOLVING OF A CONTROL PROBLEM FOR INTEGRO-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE - A.T.Assanova; E.A.Bakirova; Zh.M.Kadirbayeva (Academic Scientific Journal of Computer Science, 2019)
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.