General Framework, Stability and Error Analysis for Numerical Stiff Boundary Value Methods

Uri Ascher and R. M. Mattheij
Publishing date
July 1987
This paper provides a general framework, called "theoretical multiple shooting'', within which various, numerical methods for stiff boundary value ordinary differential problems can be analyzed. A global stability and error analysis is given, allowing (as much as possible) the specificities of an actual numerical method to come in only locally. We demonstrate the use of our results for both one-sided and symmetric difference schemes. The class of problems treated includes some with internal (e.g. "turning point'') layers.