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The computation of orbits is performed using your choice of a variety of ode solvers. Each of these has different requirements in terms of step size, tolerance levels, and so on. The solvers (sometimes called integrators) used follow.
- Euler's method: This is a very simple scheme. It is very fast, but is only of first order. This scheme is provided mostly for comparison with more accurate algorithms.
- Runge-Kutta order 4: This is a much more sophisticated algorithm that is, as its name implies, of fourth order in accuracy. It is the default solver.
- Runge-Kutta-Fehlberg order 5: This is more sophisticated yet. It may offer the best compromise of speed and accuracy of the methods provided.
- Adams-Bashforth-Moulton order 5: This is a good predictor-corrector scheme. Use it for problems that are not stiff but have expensive function evaluations, since it requires fewer function evaluations per step than one-step schemes.
- Iterated Map: This simply evaluates all functions of the vector field to get a new step in an iterated map.
Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998