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Qualitative study of the symplectic Störmer–Verlet integrator (1995)

Hardy, David J. ; Okunbor, Daniel I.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 102 (1995), S. 8978-8982

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: Symplectic numerical integrators, such as the Störmer–Verlet method, are useful in preserving properties that are not preserved by conventional numerical integrators. This paper analyzes the Störmer–Verlet method as applied to the simple harmonic model, whose generalization is an important model for molecular dynamics simulations. Restricting our attention to the one -dimensional case, both the exact solution and the Störmer–Verlet solution to this model are expressed as functions of the number of time steps taken, and then both of these functions are interpreted geometrically. The paper shows the existence of an upper bound on the error from the Störmer–Verlet method, and then an example is worked to demonstrate the closeness of this bound. © 1995 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.468951

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Canonical numerical methods for molecular dynamics simulations (1994)

Okunbor, Daniel I. ; Skeel, Robert D.

New York, NY [u.a.] : Wiley-Blackwell

Journal of Computational Chemistry 15 (1994), S. 72-79

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ISSN: 0192-8651

Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology , Computer Science

Notes: We consider the application of canonical numerical integrators to molecular dynamics simulations. Computer experiments are done to analyze the relative merits of using canonical integrators against their noncanonical counterparts. These experiments involve the study of the properties of liquid argon utilizing the Lennard-Jones interaction potential. To accomplish this comparative study of canonical and noncanonical integrators, we computed thermodynamic and structural quantities. Our results indicate that noncanonical methods, with one exception, fail miserably to conserve energy and as a consequence give poor estimates of the other quantities. Also, higher-order canonical methods may offer an advantage over the Störmer/Verlet method. © 1994 by John Wiley & Sons, Inc.

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