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Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations. (English) Zbl 1073.65552
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:
65M06Finite difference methods (IVP of PDE)
65L12Finite difference methods for ODE (numerical methods)
35L60Nonlinear first-order hyperbolic equations
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general