Numerical solution of a control problem for ordinary differential equations with multipoint integral condition

Abstract

A linear boundary value problem with a parameter for ordinary differential equations with multipoint integral conditionis investigated.The method of parameterization is used for solving the considered problem. The linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multipoint integral condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the multipoint integral condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and Runge-Kutta method of the 4-th order for solving Cauchy problem on the subintervals. A linear boundary value problem with a parameter for ordinary differential equations with multipoint integral conditionis investigated.The method of parameterization is used for solving the considered problem. The linear boundary value problem with a parameter for ordinary differential equations with multipoint integral condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multipoint integral condition and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations with respect to the parameters are composed by substituting the values of the corresponding points in the built solutions to the multipoint integral condition and the continuity condition. Numerical method for finding solution of the problem is suggested, which based on the solving the constructed system and Runge-Kutta method of the 4-th order for solving Cauchy problem on the subintervals.