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Zbl 1073.65552
Mickens, Ronald E.
Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. (English)
[J] J. Difference Equ. Appl. 11, No. 7, 645-653 (2005). ISSN 1023-6198

Summary: The need often arises to analyze the dynamics of a system in terms of a discrete formulation. This can occur by using an a priori discrete model of the system or by discretizing a continuous model. For the latter case, the continuous model is represented by differential equations and the discrete forms come from the requirement to numerically integrate these equations. The concept of ``dynamic consistency'' plays an essential role in the construction of such discrete models which usually are expressed as finite difference equations. We define this concept and illustrate its application to the construction of nonstandard finite difference schemes.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65L12 Finite difference methods for ODE
35L60 First-order nonlinear hyperbolic equations
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: nonlinear advection-reaction equation; dynamic consistency; nonstandard finite difference schemes; positivity; difference equations

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Zentralblatt MATH Berlin [Germany]