A Caltech Library Service

Long-Time Symplectic Integration: The Example of Four-Vortex Motion

Pullin, D. I. and Saffman, P. G. (1991) Long-Time Symplectic Integration: The Example of Four-Vortex Motion. Proceedings of the Royal Society of London. Series A, Mathematical, Physical and Engineering Sciences, 432 (1886). pp. 481-494. ISSN 0962-8444.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


Detailed comparisons are made between long-time numerical integration of the motion of four identical point vortices obtained using both a fourth-order symplectic integration method of the implicit Runge-Kutta type and a standard fourth-order explicit Runge-Kutta scheme. We utilize the reduced hamiltonian formulation of the four-vortex problem due to Aref & Pomphrey. Initial conditions which give both fully chaotic and also quasi-periodic motions are considered over integration times of order 10^6-10^7 times the characteristic time scale of the evolution. The convergence, as the integration time step is decreased, of the Poincare section is investigated. When smoothness of the section compared to the converged image, and the fractional change in the hamiltonian H are used as diagnostic indicators, it is found that the symplectic scheme gives substantially superior performance over the explicit scheme, and exhibits only an apparent qualitative degrading in results up to integration time steps of order the minimum timescale of the evolution. It is concluded that this performance derives from the symplectic rather than the implicit character of the method.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 1991 The Royal Society. Received 23 July 1990; accepted 9 October 1990. The authors are grateful for helpful discussions with Dr S. J. Cowley, Dr H. B. Keller, Dr J. Lorenz, Dr D. I. Meiron, Professor D. W. Moore, Dr E. Van der Velde and especially Dr A. Rouhi.
Issue or Number:1886
Record Number:CaltechAUTHORS:20141217-110551867
Persistent URL:
Official Citation:Long-Time Symplectic Integration: The Example of Four-Vortex Motion D. I. Pullin and P. G. Saffman Proceedings: Mathematical and Physical Sciences Vol. 432, No. 1886 (Mar. 8, 1991) , pp. 481-494 Published by: The Royal Society Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52960
Deposited By: Tony Diaz
Deposited On:17 Dec 2014 19:20
Last Modified:03 Oct 2019 07:46

Repository Staff Only: item control page