Package org.apache.commons.math3.ode.events

This package provides classes to handle discrete events occurring during Ordinary Differential Equations integration.

Discrete events detection is based on switching functions. The user provides a simple g(t, y) function depending on the current time and state. The integrator will monitor the value of the function throughout integration range and will trigger the event when its sign changes. The magnitude of the value is almost irrelevant, it should however be continuous (but not necessarily smooth) for the sake of root finding. The steps are shortened as needed to ensure the events occur at step boundaries (even if the integrator is a fixed-step integrator).

When an event is triggered, several different options are available:

• integration can be stopped (this is called a G-stop facility),
• the state vector or the derivatives can be changed,
• or integration can simply go on.

The first case, G-stop, is the most common one. A typical use case is when an ODE must be solved up to some target state is reached, with a known value of the state but an unknown occurrence time. As an example, if we want to monitor a chemical reaction up to some predefined concentration for the first substance, we can use the following switching function setting:

  public double g(double t, double[] y) {
    return y[0] - targetConcentration;
  }

  public int eventOccurred(double t, double[] y) {
    return STOP;
  }
 

The second case, change state vector or derivatives is encountered when dealing with discontinuous dynamical models. A typical case would be the motion of a spacecraft when thrusters are fired for orbital maneuvers. The acceleration is smooth as long as no maneuver are performed, depending only on gravity, drag, third body attraction, radiation pressure. Firing a thruster introduces a discontinuity that must be handled appropriately by the integrator. In such a case, we would use a switching function setting similar to this:

  public double g(double t, double[] y) {
    return (t - tManeuverStart) ∗ (t - tManeuverStop);
  }

  public int eventOccurred(double t, double[] y) {
    return RESET_DERIVATIVES;
  }
 

The third case is useful mainly for monitoring purposes, a simple example is:

  public double g(double t, double[] y) {
    return y[0] - y[1];
  }

  public int eventOccurred(double t, double[] y) {
    logger.log("y0(t) and y1(t) curves cross at t = " + t);
    return CONTINUE;
  }