On Stability and Accuracy of Numerical Integration Methods for Stiff Differential Equations,

Abstract

This paper surveys research concerning the stability and accuracy of numerical integration methods for stiff systems of ordinary differential equations. First, the theory of A-stability of linear multistep methods is reviewed. Second, weaker concepts of unconditional fixed-h stability are discussed. Third, examples of A-stable methods of high orders of accuracy are given. Fourth, results relating the order of accuracy to various stability concepts are listed. Fifth, some recent work concerning asymptotic stability of non-linear multistep difference equations is summarized.

Document Details

Document Type
Technical Report
Publication Date
May 06, 1976
Accession Number
ADA029728

Entities

People

  • W. Liniger

Organizations

  • IBM Thomas J. Watson Research Center

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Difference Equations
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Numerical Integration

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Systems Analysis and Design