Collocation for Two-Point Boundary Value Problems Revisited

Abstract

Collocation methods for two-point boundary value problems for higher order differential equations are considered. By using appropriate monomial bases, we relate these methods to corresponding one-step schemes for 1st order systems of differential equations. This allows us to present the theory for nonstiff problems in relatively simple terms, refining at the same time some convergence results and discussing stability. No restriction is placed on the meshes used.