General framework, stability and error analysis for numerical stiff boundary value methods (Q1116664)

This paper provides a general framework, called ``theoretical multiple shooting'' within which various numerical methods for stiff boundary value ordinary differential equations can be analyzed. A global stability and error analysis is given, allowing (as much as possible) the specifities of an actual numerical method to come in only locally. The use of the results is demonstrated for both one-sided and symmetric difference schemes. The class of problems treated includes some with internal (e.g. ``turning point'') layers.