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Time integration and Poincaré maps

MATLAB provides a suite of ODE-solvers. To create a combined integration-continuation environment, we have made them all accessible in MATCONT and added two new ones, `ode78` and `ode87`. `ode78` is an explicit Runge-Kutta method that uses 7th order Fehlberg formulas [Fehlberg 1969]. This is a 7-8th-order accurate integrator, therefore the local error normally expected is . `ode87` is a Runge-Kutta method that uses 8-7th order Dorman and Prince formulas. See [Prince and Dorman 1981]. This is a 8th-order accurate integrator therefore the local error normally expected is . In MATCONT the choice of the solver is made via the Integrator window that is opened automatically when the curve type O (Orbit) is chosen. We note that the Starter window has a SelectCycle button that allows to start the continuation of periodic orbits from curves computed by time integration.

Subsections

- Time integration
  - Solver output properties
  - Jacobian matrices
  - The Steinmetz-Larter example
- Poincaré section and Poincaré map
  - Poincaré maps in CL/SMALL>_MATCONT