FULLY DISCRETE STABILITY AND INVARIANT RECTANGULAR REGIONS FOR REACTION-DIFFUSION SYSTEMS.

Joseph W. Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Reaction-diffusion systems are considered for which the range of the initial datum is confined to a rectangular slab, on the boundary of which the reactive vector field is inward pointing. Using the variational formulation of these partial differential equations as a starting point, we may define fully discrete analogues via finite differences, provided gradient approximations and quadratures are compatibly selected. It is determined herein that such discretizations are stable, i. e. , the evolution of the discrete approximation vectors is confined to the invariant slab. The boundary conditions considered are those suited for the applications to chemically reacting and biological systems.

Original languageEnglish (US)
Pages (from-to)1054-1065
Number of pages12
JournalSIAM Journal on Numerical Analysis
Volume21
Issue number6
DOIs
StatePublished - Jan 1 1984

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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