Name
Title | ||
|---|---|---|
A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
1997 | 10.1137/S1064827595282350 | SIAM Journal on Scientific Computing |
Keywords | Field | DocType |
leapfrog,Stormer,Verlet,implicit midpoint,trapezoid,Cowell,Numerov,symplectic integrator,molecular dynamics,method of modified equations | Differential equation,Mathematical optimization,Ordinary differential equation,Midpoint,Mathematical analysis,Symplectic geometry,Symplectic integrator,Hamiltonian mechanics,Variational integrator,Mathematics,Verlet integration | Journal |
Volume | Issue | ISSN |
18 | 1 | 1064-8275 |
Citations | PageRank | References |
19 | 7.55 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robert D. Skeel | 1 | 971 | 186.69 |
| Guihua Zhang | 2 | 44 | 15.07 |
| Tamar Schlick | 3 | 251 | 62.71 |