JuliaLang/ODE.jl — pull request #10 by acroy (2014-01-27 11:46:13+00:00)
Title: WIP: symplectic solver based on velocity verlet

This PR adds two functions, `verlet_fixed` and `verlet_hh2`, which implement the velocity Verlet method with fixed and adaptive time-steps, respectively. The latter uses an estimate of the error based on comparing a full step with two half-steps. This function is exported as `verlet`.

The interface is largely compatible with the proposal in #7. The main difference is, that "velocity" and "position" are
specified (and returned) separately, instead of having one solution vector. Moreover, the acceleration (or force) currently only depends on time and position.

There are still some other things to do (absolute and relative tolerances, intermediate steps in `tspan`, ...), which partly depend on the outcome of #7.

Examples can be found here: [harmonic oscialltor](https://gist.github.com/acroy/8646927) and [pendulum](https://gist.github.com/acroy/8647126)

Comments and suggestions are very welcome.