Numerical methods for the solution of ill conditioned linear boundary value problems

Abstract

This thesis deals with the numerical solution of linear boundary valueproblems in ordinary differential equations, and it concentrates particularlyon the practical numerical difficulties encountered in the solution of illconditioned such problems.The chief methods available for the numerical solution of wellconditioned problems are described followed by a discussion of the natureof ill conditioning. The main section of the thesis is then concerned withthe techniques proposed fox tackling ill conditioned problems. These methodsare illustrated by the numerical solution of chosen test problems by meansof microcomputer programs, written especially by the author for thatpurpose, and the final section contains his conclusions based on this numericalexperience.