**$IntegralAutoStep**

$IntegralAutoStep provides an alternative to selecting the integration auto step size parameters from the Preferences dialog. The format of the $IntegralAutoStep directive is

$IntegralAutoStep Fixed=250 Richardson=Off

or

$IntegralAutoStep Vary=1 Min=50 Max=2000 Reduce=1e-3 Increase=1e-5

Integration with automatic step size is assumed when the equation-based Integral command does not include a step size or when the specified step size is zero. In either case the step size will be chosen so as to provide a fixed number of steps or according to an automatic step-size adjustment algorithm. The first form of the $IntegralAutoStep shown above specifies the fixed number of number of steps and optionally allows the Richardson extrapolation to be turned on or off.

The second form of the $IntegralAutoStep directive instructs EES to use an automatic step size adjustment algorithm that is applied every N steps where N is the number specified with the Vary keyword. The minimum and maximum step size can be specified by fixing the Minimum and Maximum number of steps with the Min and Max keywords (note minimum step size is integration time divided by the maximum number of steps specified and maximum step size is the integration time divided by the minimum number of steps specified). The step size is reduced if the relative error tolerance increased above the value provided with the Reduce keyword. The step size is increased when the relative error falls below the value provided by the Increase keyword. All of the keywords, with the exception of the Vary keyword are optional. Note that parameters must be provided with numerical constants. EES variables cannot be used to provide the integration parameter values.

The $IntegralAutoStep directive is processed when the equations are compiled and the specifications made with the directive will override any previous settings.

See also: Integration Parameters