Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

Z. Chen, Abba Gumel, R. E. Mickens

Research output: Contribution to journalArticle

23 Citations (Scopus)

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 2003
Externally publishedYes

Fingerprint

Reaction-diffusion Equations
Discretization
Runge Kutta methods
Implicit Scheme
Explicit Methods
Qualitative Analysis
Runge-Kutta Methods
Finite difference method
Difference Method
Fourth Order
Euler
Stability Analysis
Finite Difference
Numerical Solution
Numerical Simulation
Computer simulation
Standards

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation. / Chen, Z.; Gumel, Abba; Mickens, R. E.

In: Numerical Methods for Partial Differential Equations, Vol. 19, No. 3, 05.2003, p. 363-379.

Research output: Contribution to journalArticle

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