Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

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

doi:10.1002/num.10048

Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

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

Research output: Contribution to journal › Article › peer-review

37 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 language	English (US)
Pages (from-to)	363-379
Number of pages	17
Journal	Numerical Methods for Partial Differential Equations
Volume	19
Issue number	3
DOIs	https://doi.org/10.1002/num.10048
State	Published - May 2003
Externally published	Yes

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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10.1002/num.10048

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AB - 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.

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KW - Nonstandard finite-difference schemes

KW - Positivity

KW - Truncation errors

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Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

Abstract

Keywords

ASJC Scopus subject areas

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