ON THE SOLVABILITY OF A MULTIPOINT BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EQUATIONS

This paper investigates the solvability of a linear multipoint boundary value problem for a system of loaded differential equations. The study is carried out using Dzhumabaev parameterization method, which reduces the original boundary value problem to an equivalent system of algebraic equations and Cauchy problems for ordinary differential equations. Based on this approach, sufficient conditions for the existence and uniqueness of a solution are established. An iterative algorithm for constructing the solution is proposed, and its convergence is proved under the derived assumptions. The practical implementation of the method is demonstrated on a model example, where the Cauchy problems arising in the procedure are solved numerically using the fourth-order Runge-Kutta method. The results confirm the efficiency and high convergence rate of the proposed approach. 

multipoint boundary value problem, loaded differential equation, parameterization method, algorithm, solvability

ON THE SOLVABILITY OF A MULTIPOINT BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EQUATIONS