Exact finite difference and non-standard finite difference schemes for

DOI10.1080/10236198.2011.574622zbMath1260.65072OpenAlexW2034710653MaRDI QIDQ3165731

Lih-Ing W. Roeger, Ronald E. Mickens

Publication date: 19 October 2012

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2011.574622

zbMATH Keywords

initial value problemsfinite difference schemesexact integrationnon standard schemes

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (11)

Nonstandard finite difference schemes for a class of generalized convection–diffusion–reaction equations ⋮ A non‐standard finite difference scheme for an advection‐diffusion‐reaction equation ⋮ On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation ⋮ Dynamics of a nonstandard finite-difference scheme for a limit cycle oscillator with delayed feedback ⋮ A fast and unconditionally positive finite-difference discretization of a multidimensional equation in nonlinear population dynamics ⋮ An exact finite difference scheme for a three-layer beam model ⋮ Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation ⋮ Exact finite difference schemes for three-dimensional linear systems with constant coefficients ⋮ On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation ⋮ Exact finite difference scheme for linear differential equation with constant coefficients ⋮ A Mickens-type monotone discretization for bounded travelling-wave solutions of a Burgers–Fisher partial differential equation^a*

Cites Work

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• Preservation of local dynamics when applying central difference methods: application to SIR model
• Nonstandard finite difference schemes for differential equations withn+1 distinct fixed-points
• Studies in Numerical Nonlinear Instability I. Why do Leapfrog Schemes Go Unstable?
• Dynamically consistent discrete Lotka–Volterra competition systems
• Differential and Difference Equations

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