Faster integration of the equations of motion
ACM SIGGRAPH 98 Conference abstracts and applications
Scalable Molecular-Dynamics, Visualization, and Data-Management Algorithms for Materials Simulations
Computing in Science and Engineering
Nonlinear instability in multiple time stepping molecular dynamics
Proceedings of the 2003 ACM symposium on Applied computing
A Rigid-Body-Based Multiple Time Scale Molecular Dynamics Simulation of Nanophase Materials
International Journal of High Performance Computing Applications
Stability of Asynchronous Variational Integrators
Proceedings of the 21st International Workshop on Principles of Advanced and Distributed Simulation
Stability of asynchronous variational integrators
Journal of Computational Physics
Overview of molecular dynamics techniques and early scientific results from the Blue Gene project
IBM Journal of Research and Development
DFT modal analysis of spectral element methods for the 2D elastic wave equation
Journal of Computational and Applied Mathematics
| Hi-index | 0.01 |
The following integration methods for special second-order ordinary differential equations are studied: leapfrog, implicit midpoint, trapezoid, Störmer--Verlet, and Cowell--Numerov. We show that all are members, or equivalent to members, of a one-parameter family of schemes. Some methods have more than one common form, and we discuss a systematic enumeration of these forms. We also present a stability and accuracy analysis based on the idea of "modified equations" and a proof of symplecticness. It follows that Cowell--Numerov and "LIM2" (a method proposed by Zhang and Schlick) are symplectic. A different interpretation of the values used by these integrators leads to higher accuracy and better energy conservation. Hence, we suggest that the straightforward analysis of energy conservation is misleading.