An Examination of Stability Criteria for Iterative Numerical Schemes Used in Solving Differential Equations

Abstract

The stability of numerical schemes for solving algebraic finite- difference equations resulting from finite-difference approximations to differential equations is discussed. It is suggested that the von Neumann method together with its stability criterion provides a reasonably simple way of determining stability. However, there are limitations in its applicability, some of which are indicated. The method is tested in two examples and an indication is given of how best to treat first- and mixed-derivative terms occurring in differential equations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA109362

Entities

People

  • Katharine Moore

Organizations

  • Royal Aircraft Establishment

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Amplification
  • Boundaries
  • Capillary Electrophoresis
  • Coefficients
  • Convergence
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Grids
  • Instability
  • Iterations
  • Linear Differential Equations
  • Matrix Theory
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

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