Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

Z. Chen, A. B. Gumel, R. E. Mickens

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

A competitive nonstandard semi-explicit finite-difference method is constructed and used to obtain numerical solutions of the diffusion-free generalized Nagumo equation. Qualitative stability analysis and numerical simulations show that this scheme is more robust in comparison to some standard explicit methods such as forward Euler and the fourth-order Runge-Kutta method (RK4). The nonstandard scheme is extended to construct a semi-explicit and an implicit scheme to solve the full Nagumo reaction-diffusion equation.

Original languageEnglish (US)
Pages (from-to)363-379
Number of pages17
JournalNumerical Methods for Partial Differential Equations
Volume19
Issue number3
DOIs
StatePublished - May 1 2003
Externally publishedYes

Keywords

  • Convergence
  • Nagumo model
  • Nonstandard finite-difference schemes
  • Positivity
  • Truncation errors

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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