Are Gauss-Legendre methods useful in molecular dynamics?
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.
scientific article; zbMATH DE number 908364
scientific article