Class MultistepIntegrator

  • All Implemented Interfaces:
    FirstOrderIntegrator, ODEIntegrator
    Direct Known Subclasses:

    public abstract class MultistepIntegrator
    extends AdaptiveStepsizeIntegrator
    This class is the base class for multistep integrators for Ordinary Differential Equations.

    We define scaled derivatives si(n) at step n as:

     s1(n) = h y'n for first derivative
     s2(n) = h2/2 y''n for second derivative
     s3(n) = h3/6 y'''n for third derivative
     sk(n) = hk/k! y(k)n for kth derivative

    Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (yn, s1(n) and rn) where rn is defined as:

     rn = [ s2(n), s3(n) ... sk(n) ]T
    (we omit the k index in the notation for clarity)

    Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by a factor a, the kth component of the Nordsieck vector is multiplied by ak and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 21/order.

    See Also:
    AdamsBashforthIntegrator, AdamsMoultonIntegrator
    • Method Detail

      • getStarterIntegrator

        public ODEIntegrator getStarterIntegrator()
        Get the starter integrator.
        starter integrator
      • setStarterIntegrator

        public void setStarterIntegrator​(FirstOrderIntegrator starterIntegrator)
        Set the starter integrator.

        The various step and event handlers for this starter integrator will be managed automatically by the multi-step integrator. Any user configuration for these elements will be cleared before use.

        starterIntegrator - starter integrator
      • getMinReduction

        public double getMinReduction()
        Get the minimal reduction factor for stepsize control.
        minimal reduction factor
      • setMinReduction

        public void setMinReduction​(double minReduction)
        Set the minimal reduction factor for stepsize control.
        minReduction - minimal reduction factor
      • getMaxGrowth

        public double getMaxGrowth()
        Get the maximal growth factor for stepsize control.
        maximal growth factor
      • setMaxGrowth

        public void setMaxGrowth​(double maxGrowth)
        Set the maximal growth factor for stepsize control.
        maxGrowth - maximal growth factor
      • getSafety

        public double getSafety()
        Get the safety factor for stepsize control.
        safety factor
      • setSafety

        public void setSafety​(double safety)
        Set the safety factor for stepsize control.
        safety - safety factor