The Difference Correction Method for Non-Linear Two-Point Boundary Value Problems

摘要

The numerical solution of non-linear two-point boundary value problems is discussed. It is shown that for a certain class of finite difference approximations the a posteriori use of a difference correction raises the order of the approximation by at least two orders. The difference correction itself involves only the solution of one system of linear equations. If Newton's method is used in the early stage, then it is shown that the matrices in both processes are identical, which is a useful feature in coding the method for an automatic computer. Several numerical examples are given. (Author)