LINEAR Multistep Methods with Near-Optimal Stability
Abstract
Desirable properties of linear multistep methods (LMM) can be optimized by viewing those properties as functional values and the LMM possessing those properties as points in a domain space. This study conducts two such optimizations numerically. The first is a search for relatively stable explicit LMM and the second is a search for stiffly stable implicit LMM. Near- optimally relatively stable explicit LMM are found for orders four through nine. In the second study, the concept of A(alpha, r)-stability is introduced for stiffly stable LMM. It recognizes the need for large regions of absolute stability in the left half plane and the need for a region of accuracy about the origin defined by the region of relative stability. An economical means of determining the region of relative stability is developed and used.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1979
- Accession Number
- ADA091008
Entities
People
- David J. Nolting
Organizations
- Air Force Institute of Technology