A Unified View of Some Methods for Stiff Two-Point Boundary Value Problems,
Abstract
The paper analyses a number of known methods for the solution of two point boundary value problems for ordinary differential equations; the methods considered have in common that they lead to a sequence of initial value problems. A routine approach fails if the differential equations are stiff. In geometric terms, all methods perform the same basic task; they determine a sequence of loci in a vector space to which the solution is confined. Even in stiff equations the loci are well defined, but the vectors used to describe them have a tendency to become more and more parallel unless one takes special measures. The method of Godunov-Conte and the parallel shooting method of Keller periodically change the basis used for the representation of the loci; the method of Guderley-Nikolai introduces an x dependent representation for the loci which changes only if subspaces parallel to them change. In this manner the loss of accuracy can be controlled by all methods. (Modified author abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1973
- Accession Number
- AD0769479
Entities
People
- Karl G. Guderley
Organizations
- Air Force Research Laboratory