A method for high-order multipoint boundary value problems with Birkhoff-type conditions.

In this paper an efficient numerical method for solving a class of multipoint boundary value problems with special boundary conditions of Birkhoff-type is presented. After a quick reference to Birkhoff-type interpolation polynomial which satisfies the particular conditions, and a result on the existence and uniqueness of solution of the given problem, an algorithm is introduced to find a polynomial that approximates the solution. It is a general collocation method. Then an a priori estimation of the error of this approximation is given. Finally, to show the efficiency and the applicability of the method, numerical results are presented. These numerical experiments provide favourable comparisons with the NDSolve command of Mathematica. [ABSTRACT FROM AUTHOR]