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On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method

On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the... In the present paper, we discuss the problem on the total energy conservation for the numerical solution of the Cauchy problem for the equations of classical molecular dynamics by symplectic and symmetric methods. We consider the methods from a one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method. In particular, we show that a numerical algorithm preserving the total energy of the system on the approximate solutions of the model Cauchy problem almost on the entire trajectory can be constructed on the basis of the one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method

Elenin, G.; Shlyakhov, P.
Differential Equations , Volume 46 (7) – Aug 18, 2010
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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266110070062
Publisher site
See Article on Publisher Site

Abstract

In the present paper, we discuss the problem on the total energy conservation for the numerical solution of the Cauchy problem for the equations of classical molecular dynamics by symplectic and symmetric methods. We consider the methods from a one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method. In particular, we show that a numerical algorithm preserving the total energy of the system on the approximate solutions of the model Cauchy problem almost on the entire trajectory can be constructed on the basis of the one-parameter family of two-stage symmetric-symplectic Runge-Kutta methods.

Journal

Differential Equations – Springer Journals

Published: Aug 18, 2010

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