Are Gauss-Legendre methods useful in molecular dynamics?
type: Item
instance of: scholarly article
title: Are Gauss-Legendre methods useful in molecular dynamics?
zbMATH Open document ID: 0856.65083
DOI: 10.1016/0377-0427(95)00151-4
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 1997-02-24T00:00:00Z
review text: This paper is concerned with the application of the symplectic two-stage Gauss-Legendre method to the numerical solution of typical integration of molecular dynamics. As remarked by the authors, the main features of these problems are its high dimensionality and its Hamiltonian character. Thus, to capture the dynamics of the solutions the numerical integrators are usually based on symplectic formulas and traditionally the Verlet method [cf. \textit{M. P. Allen} and \textit{D. J. Tildesley}, Computer simulation of liquids (1987; Zbl 0703.68099)] has been used for the numerical solution of these problems. Verlet's method has low computational cost per step and it has low storage requirements but due to its low order, to increase the accuracy of the computations on long intervals the cost becomes very high. In view of this fact, the authors propose to study the potentiality of the higher-order symplectic two-stage Gauss-Legendre method for such problems. As a consequence of their numerical experiments they conclude that Gauss-Legendre methods are less efficient than Verlet's method for the standard ranges of accuracy required for these problems. However, in the case of very stringent accuracy requirements the Gauss-Legendre method turns out to be competitive with Verlet's method.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 81V55
zbMATH DE Number: 908364
zbMATH Keywords: molecular dynamics
zbMATH Keywords: Hamiltonian
zbMATH Keywords: symplectic formulas
zbMATH Keywords: Verlet method
zbMATH Keywords: Gauss-Legendre method
zbMATH Keywords: numerical experiments
reviewed by: Manuel Calvo
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00151-4
OpenAlex ID: W1993554648
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description: scientific article; zbMATH DE number 908364