Indirect methods for the numerical solution of ordinary linear boundary value problems

Abstract

This thesis is mainly concerned with indirect numerical solution methods for linear two point boundary value problems. We concentrate particularly on problems with separated boundary conditions which have a 'dichotomy' property. We investigate the inter-relationship of various methods including some which have first appeared since the work for this thesis began. We examine the stability of these methods and in particular we consider circumstances in which the methods discussed give rise to well conditioned decoupling transformations. Empirical comparisons of some of the methods are described using a set of test problems including a number of ill conditioned problams. 'stiff' and marginally In the past the main method of error estimation has been to repaat the whole calculation. Here an alternative error estimation technique is proposed and a related iterative improvement method is considered. Although results for this are not completely conclusive we think they justify the need for further research on the method as it shows promise of being a novel and reliable practical method of solving both well conditioned and ill conditioned problems.