An effective computational method for solving linear multi-point boundary value problems

In this work, an efficient computational method is proposed for solving the linear multi-point boundary value problems (MBVPs). Our approach depends mainly on of the least squares approximation method, the Lagrange-multiplier method and the residual error function technique. With the proposed scheme, we handle the numerical solutions of the linear MBVPs in a straightforward manner. Firstly, the given linear MBVP is reduced to a linear system of algebraic equations, and the coefficients of the approximate polynomial solution of the problem are determined by solving this system. Secondly, a linear boundary value problem related to the error function of the approximate solution is constructed, and error estimation is presented for the suggested method. The convergence of the approximate solution is proved. The reliability and efficiency of the proposed approach are demonstrated by some numerical examples.