STABILITY ANALYSIS OF FINITE-DIFFERENCE SCHEMES FOR THE ADVECTION-DIFFUSION EQUATION.

Tony Chan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

A collection of stability results for finite difference approximations to the advection-diffusion equation u//t equals au//x bu//x//x is presented. The results are for centered difference schemes in space and include explicit and implicit 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.

Original languageEnglish (US)
Pages (from-to)272-284
Number of pages13
JournalSIAM Journal on Numerical Analysis
Volume21
Issue number2
DOIs
StatePublished - Jan 1 1984

ASJC Scopus subject areas

  • Numerical Analysis

Fingerprint

Dive into the research topics of 'STABILITY ANALYSIS OF FINITE-DIFFERENCE SCHEMES FOR THE ADVECTION-DIFFUSION EQUATION.'. Together they form a unique fingerprint.

Cite this