Stability Analysis of Finite Difference Schemes for the Advection-Diffusion Equation,

Abstract

We present a collection of stability results for finite difference approximations to the advection-diffusion equation sub ut = a sub ux + b sub uxx. The results are for centered difference schemes in space and include explicit schemes in time up to fourth order and schemes that use different space and time discretizations for the advective and diffusive terms. The results are derived from a uniform framework based on the Schur-Cohn theory of simple von Neumann Polynomials and are necessary and sufficient for the stability of the Cauchy problem. Some of the results are believed to be new. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1983
Accession Number
ADA126082

Entities

People

  • Tony F. Chan

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Difference Equations
  • Differential Equations
  • Equations
  • Fluid Dynamics
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Stability Conditions
  • Theorems
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space