A Search for Better Linear Multistep Methods for Stiff Problems

Abstract

For arbitrary k >/- 1 and alpha epsilon (O,pi/2), A(alpha)-stable k-th order k-step formulas exist, so that in an ODE solver, a can be an extra parameter used to identify among a family of methods of order k the A(alpha)-stable method that should be used for the particular problem. Two measures for assessing the accuracy of k-th order k-step formulas are proposed. The problem of finding the upper bound on the angle of absolute stability for the k-th order k-step formulas having the same accuracy (with respect to one of the measures) is considered. Analytical results are obtained for k = 1, 2, 3 whereas a numerical search is used for the cases when k = 4, 5, 6, 7.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA374153

Entities

People

  • Antony King-yin Kong

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Cyber

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Command And Control
  • Command Control Communications
  • Complex Variables
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Difference Equations
  • Differential Equations
  • Equations
  • Linear Algebra
  • New York
  • Numerical Analysis
  • Plastic Explosives
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Game Theory.