Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator.

Abstract

[EN]This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval.The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme.