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On energy conservation of the simplified Takahashi-Imada method

Ernst Hairer, Robert I. McLachlan, Robert D. Skeel (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy to implement...

One-Parameter Bifurcation Analysis of Dynamical Systems using Maple

Borisov, Milen, Dimitrova, Neli (2010)

Serdica Journal of Computing

This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.

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