Numerical Methods for Stiff Nonlinear and Quadratic Differential Equations.

Abstract

First, results are given concerning input-output stability and Liapunov variational stability of nonlinear multistep difference equations. They state that formulas which are A-stable, or possess other similar linear properties of unconditional fixed-h stability, are stable also when applied to certain representative classes/of (eg, monotone) nonlinear differential systems. Second, a description is presented of the design, implementation, and testing of a collection of highly-accurate, A-stable and nonlinearly stable integration algorithm based on averaging. Third, results are provided establishing some basic theoretical properties of fractional linear difference schemes for the solution of systems of quadratic differential equations.

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1976
Accession Number
ADA025200

Entities

People

  • W. Liniger

Organizations

  • IBM Thomas J. Watson Research Center

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Difference Equations
  • Differential Equations
  • Equations
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)