http://popups.lib.uliege.be/1373-5411/index.php?id=1474 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=2428 This paper deals with a comparison from the precision and stability point of view of different discrete algorithms for simulating differential equation systems, applied in the case of a simple differential system: the harmonic oscillator. It points out the relation between the classical and incursive algorithms and shows the effect of incursion on the precision and stability. Tue, 20 Aug 2024 11:46:18 +0200 Tue, 08 Oct 2024 13:34:57 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2428 http://popups.lib.uliege.be/1373-5411/index.php?id=2597 This paper deals with anticipatory systems and their use when describing the population dynamics of single species discrete systems. In doing so, it starts from Rosen's original definition of anticipatory system and its extending in the papers of Dubois. Then the concepts of incursion and hyperincursion are briefly explained and their applications to modeling discrete dynamic systems are outlined. A detailed analysis is given of the population model described by the first order difference equation, where the relative population size at future time is a cubic polynomial function of the population size at the present. Consequently, the corresponding in cursive and hyperincursive models are formulated and the stability of their equilibrium solutions (trajectories) is studied. Thu, 29 Aug 2024 14:55:46 +0200 Thu, 29 Aug 2024 14:55:54 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2597 http://popups.lib.uliege.be/1373-5411/index.php?id=1471 The discrete path approach has recently been use to obtain a closed form solution for two simultaneous difference equations with variable coefficients. We apply this result to the solution of the discretized harmonic oscillator and recover the well known traditional solutions. In the process we learn how the enumerative discrete path solution transforms into a more convenient compact analytic closed form. The discrete path approach is specially adapted to problems with mixed boundary conditions like those arising in the modeling of anticipatory systems. Fri, 12 Jul 2024 15:04:38 +0200 Fri, 12 Jul 2024 15:04:46 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1471