Numerical Hamiltonian Problems

Sanz‐Serna, J. M.; Calvo, M. P.

doi:10.1007/978-1-4899-3093-4

Cited by 1,068 publications

(854 citation statements)

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“…From this we can see that we are dealing with a Hamiltonian system with Hamiltonian -'ljJ. A very important property of such a system is the concept of preservation of area (see [9]) which in our case is equivalent to conservation of mass. Operators which have this property, are called symplectic.…”

Section: Y(t) -V(x Y T) Andv(xyt) Andxmentioning

confidence: 96%

Contour Dynamics with Symplectic Time Integration

Vosbeek

Mattheij

1997

Journal of Computational Physics

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In this paper we consider the time evolution of vortices simulated by the method of contour dynamics. Special attention is being paid to the Hamiltonian character of the governing equations and in particular to the conservational properties of numerical time integration for them. We assess symplectic and non-symplectic schemes. For the former methods, we give an implementation which is both efficient and yet effectively explicit. A number of numerical examples sustain the analysis and demonstrate the usefulness of the approach.

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Section: Y(t) -V(x Y T) Andv(xyt) Andxmentioning

confidence: 96%

Contour Dynamics with Symplectic Time Integration

Vosbeek

Mattheij

1997

Journal of Computational Physics

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“…Standard results from the backward error analysis of numerical integrators [15,9] show then the existence of an autonomous system (the modified system of Ψ t 0 ;ε )…”

Section: A Modified Equation Approach To Averagingmentioning

confidence: 99%

A Stroboscopic Numerical Method for Highly Oscillatory Problems

Calvo

Chartier

Murua³

et al. 2011

Lecture Notes in Computational Science and Engineering

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We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging. The technique may be easily implemented in combination with standard software and may be applied with variable step sizes. Numerical experiments show that the suggested algorithms may be substantially more efficient than standard numerical integrators.

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“…We use Eqs. (4) as initial conditions to integrate the dynamical equations using a symplectic algorithm [13].…”

Section: Introduction and Model Set-upmentioning

confidence: 99%

Moving Breather Collisions in the Peyrard-Bishop DNA Model

Álvarez

Romero

Cuevas

et al. 2009

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Abstract. We consider collisions of moving breathers (MBs) in the Peyrard-Bishop DNA model. Two identical stationary breathers, separated by a fixed number of pair-bases, are perturbed and begin to move approaching to each other with the same module of velocity. The outcome is strongly dependent of both the velocity of the MBs and the number of pair-bases that initially separates the stationary breathers. Some collisions result in the generation of a new stationary trapped breather of larger energy. Other collisions result in the generation of two new MBs. In the DNA molecule, the trapping phenomenon could be part of the complex mechanisms involved in the initiation of the transcription processes.

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Numerical Hamiltonian Problems

Cited by 1,068 publications

References 0 publications

Contour Dynamics with Symplectic Time Integration

Contour Dynamics with Symplectic Time Integration

A Stroboscopic Numerical Method for Highly Oscillatory Problems

Moving Breather Collisions in the Peyrard-Bishop DNA Model

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