A collocation method for two-point boundary value problems

Abstract

This article is concerned with the use of collocation by splines to numerically solve two-point boundary value problems. The problem is analyzed in terms of cubic splines first and then extended to the use of quintic and septic splines. Consideration is given both to convergences as the mesh is refined and to the bandwidth of the matrices involved. Comparisons are made to a similar approach using the Galerkin method rather than collocation.