Code available for boundary-value problems

Abstract

In a series of well-known papers, Victor Pereyra and colleagues have developed the deferred-correction of divided-difference methods for the numerical solution of two-point boundary-value problems both for first-order systems and for second-order scalar equations. As a first step on the road similarly to developing deferred-correction of collocation methods, we have studied Pereyra's code IDCBVP for the second-order case in detail; since most of Pereyra's effort has been directed toward first-order systems, it is not surprising that we were able to improve IDCBVP considerably. Such effort seems worthwhile since experience indicates that for efficiency one should solve second-order problems as second-order problems rather than as first-order systems. Our resulting code NUMIDC is efficient, accurate, reliable, and seems to compare favorably with competing codes on appropriate problems.