Abstract
Symplectic numerical integrators, such as the Stormer-Verlet method, are useful in preserving certain important properties that are not preserved by conventional numerical integrators. This paper analyzes the Stormer-Verlet method as applied to the simple harmonic model, which is an important model for molecular dynamics simulations. Restricting our attention to the one-dimensional case, both the exact solution and the Stormer-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 Stormer-Verlet method, and then an example is worked to demonstrate the closeness of this bound.
Recommended Citation
Hardy, D. J. and Okunbor, D. I., "Qualitative Study of the Symplectic Stormer-Verlet Integrator" (1994). Computer Science Technical Reports. 175.
https://scholarsmine.mst.edu/comsci_techreports/175
Department(s)
Computer Science
Keywords and Phrases
Hamiltonian systems, energy conservation, symplectic integrators
Report Number
CSc-94-26
Document Type
Technical Report
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 1994 University of Missouri - Rolla, All rights reserved
Publication Date
1 June, 1994
Comments
Both of the Authors are Graduate Students.
Supported in part by the University of Missouri-Rolla and by the National Science Foundation Grant CCR-9408973.