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.

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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

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Coefficients
  • Computations
  • Computers
  • Convergence
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Eigenvalues
  • Equations
  • Error Analysis
  • Errors
  • Plastic Explosives
  • Precision
  • Test And Evaluation

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra

Technology Areas

  • Space