A Comparison of Collocation and Finite Differences for Two-Point Boundary Value Problems

Abstract

A comparison of certain $O(h^4 )$ and $O(h^6 )$ collocation and finite difference methods is made for a second order two-point boundary value problem. On the basis of operation counts, we conclude that collocation is generally competitive if evaluation of basis functions and stable solution of the linear systems are done carefully. Collocation using smooth splines has some useful features, although certain approximation difficulties are encountered in the numerical examples.