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Discrete-time and continuous-time modelling: some bridges and gaps


The relationship between continuous-time dynamics and the corresponding discrete schemes, and its generally limited validity, is an important and widely acknowledged field within numerical analysis. In this paper, we propose another, more physical, viewpoint on this topic in order to understand the possible failure of discretisation procedures and the way to fix it. Three basic examples, the logistic equation, the Lotka–Volterra predator–prey model and Newton's law for planetary motion, are worked out. They illustrate the deep difference between continuous-time evolutions and discrete-time mappings, hence shedding some light on the more general duality between continuous descriptions of natural phenomena and discrete numerical computations.

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E. Hairer , C. Lubich and G. Wanner (2002) Geometric numerical integration, Springer.

J. Hubbard and B. West (1991) Differential equations, a dynamical systems approach, Springer.

H. O. Peitgen , H. Jürgens and D. Saupe (1992) Chaos and fractals, Springer.

M. Yamaguti and H. Matano (1979) Euler's finite difference scheme and chaos. Proc. Japan Acad. Series A 55 7880.

A. J. Lotka (1920) Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. USA 6 410415.

R. M. May (1976) Simple mathematical models with very complicated dynamics. Nature 261 459467.

J. M. Sanz-Serna (1992) Symplectic integrators for Hamiltonian problems: an overview. Acta Numerica 1 243286.

D. J. Evans and G. P. Morriss (1990) Statistical mechanics of nonequilibrium liquids, Chapter 10, Academic Press.

M. Feigenbaum (1978) Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19 2552.

E. Mendes and C. Letellier (2004) Displacement in the parameter space versus spurious solution of discretization with large time step. J. Phys. A 37 12031218.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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