WhenEvent—Wolfram Mathematica 9 Documentation

Details and Options Details and Options

In NDSolve[eqns, ...] the WhenEvent expressions are included in eqns and can be considered a part of the specification for the solution, especially for piecewise or hybrid systems.
At a time when the event becomes True, the action is evaluated with the numerical solution values at . Examples of events and how is determined include:

	pred	the predicate pred becomes True
	f=0	the function f of the solution variables crosses zero
	f>0	f crosses zero from below
	f<0	f crosses zero from above
	f=0&&pred	f crosses zero and pred is True
	Mod[t,]=0	sample at regular intervals in the time variable

WhenEvent typically finds a function f of the solution variables such that the roots of f occur where the event becomes True, and a bracketing interval within the accuracy and precision tolerances of the numerical computation is found using a numerical root-finding procedure.
In the case that a root function cannot be determined, the bracketing interval is found using bisection.
WhenEvent[{event₁, ...}, action] is treated as .
With WhenEvent[event, {action₁, action₂, ...}], the actions are evaluated sequentially.
The value from the evaluation of action is ignored by WhenEvent unless it has a special value that is used to affect NDSolve. The following special values are recognized:

	"StopIntegration"	stop integrating at , return the solution
	"RestartIntegration"	restart the integration at
	"CrossDiscontinuity"	integrate to , extrapolate, and restart at
	"CrossSlidingDiscontinuity"	integrate to , extrapolate and check sliding mode conditions, and restart at
	"RemoveEvent"	remove the event
	y[t]->val	change the state variable y to val
	d[t]->"DiscontinuitySignature"	change the discontinuity signature variable d

With WhenEvent[f==0, d->"DiscontinuitySignature"], the discontinuity is the surface f==0, and d must be a discrete variable that takes on values or and is effectively set to Sign[f] for subsequent to the event.
WhenEvent has attribute HoldAll, so by default the event and action are only evaluated with variables assigned approximated values.
WhenEvent can take the following options:

"DetectionMethod"	Automatic	the method to use for detecting an event
"LocationMethod"	Automatic	the method to use for locating an event within a time step
"IntegrateEvent"	Automatic	whether to integrate the event function
"Priority"	Automatic	priority for actions of simultaneous events

	Automatic	automatically determine detection method
	"Sign"	use a sign change
	"DerivativeSign"	use sign change and time derivative
	"Interpolation"	use interpolation of dense solution output

The detection method has the least overhead, but may miss events in rapidly varying functions. The detection method is more robust and may detect multiple events per step.
Possible settings for are:

	Automatic	automatically determine location method
	"StepBegin"	locate the event at the beginning of a step
	"StepEnd"	locate the event at the end of a step
	"LinearInterpolation"	linearly interpolate within a step
	"Brent"	use Brent's root location within a step

Possible settings for are:
Automatic automatically determined

False do not integrate the event function

True integrate the event function
The settings for can be any integer or Infinity. In the case of simultaneous events, the actions will be evaluated in sorted priority order.