The Alternating Group Iterative Algorithm Of High Order Difference Scheme For Two Point Boundary Problem

A kind of new parallel iterative algorithm for solving two point boundary value problem is constructed in this paper. The basic idea is to divide the system of difference equations into a set of subsystem that can be solved individually in parallel. The process of constructing the algorithm is given. The property of convergence is proved by matrix theory. The results of numerical experiment of some examples are obtained. It shows that the analysis is correct and the algorithm is feasible and efficient.In the end of the paper, we point out problems unsolved and indicate direction of research in the future.