Nonstandard finite difference schemes for Michaelis–Menten type reaction‐diffusion equations

DOI10.1002/num.21733zbMath1255.65141OpenAlexW2148087925MaRDI QIDQ4903223

Ronald E. Mickens, Michael Chapwanya, Jean M.-S. Lubuma

Publication date: 21 January 2013

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.21733

zbMATH Keywords

advection-reaction-diffusion equationsexact schemenonstandard finite difference methodLambert W functionMichaelis--Menten equation

Mathematics Subject Classification ID

Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (13)

An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations ⋮ Positivity-preserving nonstandard finite difference schemes for cross-diffusion equations in biosciences ⋮ An explicit nonstandard finite difference scheme for the Allen–Cahn equation ⋮ A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models ⋮ Numerical dynamics of nonstandard finite difference schemes for a logistics model with feedback control ⋮ Pattern formation in the Holling-Tanner predator-prey model with predator-taxis. A nonstandard finite difference approach ⋮ Exact and nonstandard finite difference schemes for the Burgers equationB(2,2) ⋮ Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order ⋮ Universal approaches to approximate biological systems with nonstandard finite difference methods ⋮ From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes ⋮ Nonstandard finite difference methods: recent trends and further developments ⋮ Exact and nonstandard finite difference schemes for the generalized KdV-Burgers equation ⋮ Global stability for the continuous and discrete SIS-diffusion epidemiological models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamically-consistent non-standard finite difference method for an epidemic model
• From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes
• Positive and elementary stable nonstandard numerical methods with applications to predator-prey models
• Enzyme kinetics at high enzyme concentration
• Mathematical biology. Vol. 1: An introduction.
• On non-standard finite difference models of reaction-diffusion equations
• On the Lambert \(w\) function
• Contributions to the mathematics of the nonstandard finite difference method and applications
• An exact discretization of Michaelis–Menten type population equations
• Topological dynamic consistency of non-standard finite difference schemes for dynamical systems
• The Quasi-Steady-State Assumption: A Case Study in Perturbation
• Solving singularly perturbed advection–reaction equations via non‐standard finite difference methods
• Advances in the Applications of Nonstandard Finite Difference Schemes

This page was built for publication: Nonstandard finite difference schemes for Michaelis–Menten type reaction‐diffusion equations