Class AdamsIntegrator

All Implemented Interfaces:
FirstOrderIntegrator, ODEIntegrator
Direct Known Subclasses:
AdamsBashforthIntegrator, AdamsMoultonIntegrator

public abstract class AdamsIntegrator extends MultistepIntegrator
Base class for Adams-Bashforth and Adams-Moulton integrators.
Since:
2.0
Version:
$Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $
  • Constructor Details

    • AdamsIntegrator

      public AdamsIntegrator(String name, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) throws IllegalArgumentException
      Build an Adams integrator with the given order and step control prameters.
      Parameters:
      name - name of the method
      nSteps - number of steps of the method excluding the one being computed
      order - order of the method
      minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
      maxStep - maximal step (must be positive even for backward integration)
      scalAbsoluteTolerance - allowed absolute error
      scalRelativeTolerance - allowed relative error
      Throws:
      IllegalArgumentException - if order is 1 or less
    • AdamsIntegrator

      public AdamsIntegrator(String name, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) throws IllegalArgumentException
      Build an Adams integrator with the given order and step control parameters.
      Parameters:
      name - name of the method
      nSteps - number of steps of the method excluding the one being computed
      order - order of the method
      minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
      maxStep - maximal step (must be positive even for backward integration)
      vecAbsoluteTolerance - allowed absolute error
      vecRelativeTolerance - allowed relative error
      Throws:
      IllegalArgumentException - if order is 1 or less
  • Method Details

    • integrate

      public abstract double integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) throws DerivativeException, IntegratorException
      Integrate the differential equations up to the given time.

      This method solves an Initial Value Problem (IVP).

      Since this method stores some internal state variables made available in its public interface during integration (ODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

      Specified by:
      integrate in interface FirstOrderIntegrator
      Specified by:
      integrate in class AdaptiveStepsizeIntegrator
      Parameters:
      equations - differential equations to integrate
      t0 - initial time
      y0 - initial value of the state vector at t0
      t - target time for the integration (can be set to a value smaller than t0 for backward integration)
      y - placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0
      Returns:
      stop time, will be the same as target time if integration reached its target, but may be different if some EventHandler stops it at some point.
      Throws:
      DerivativeException - this exception is propagated to the caller if the underlying user function triggers one
      IntegratorException - if the integrator cannot perform integration
    • initializeHighOrderDerivatives

      protected Array2DRowRealMatrix initializeHighOrderDerivatives(double[] first, double[][] multistep)
      Initialize the high order scaled derivatives at step start.
      Specified by:
      initializeHighOrderDerivatives in class MultistepIntegrator
      Parameters:
      first - first scaled derivative at step start
      multistep - scaled derivatives after step start (hy'1, ..., hy'k-1) will be modified
      Returns:
      high order scaled derivatives at step start
    • updateHighOrderDerivativesPhase1

      public Array2DRowRealMatrix updateHighOrderDerivativesPhase1(Array2DRowRealMatrix highOrder)
      Update the high order scaled derivatives for Adams integrators (phase 1).

      The complete update of high order derivatives has a form similar to:

       rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn
       
      this method computes the P-1 A P rn part.

      Parameters:
      highOrder - high order scaled derivatives (h2/2 y'', ... hk/k! y(k))
      Returns:
      updated high order derivatives
      See Also:
    • updateHighOrderDerivativesPhase2

      public void updateHighOrderDerivativesPhase2(double[] start, double[] end, Array2DRowRealMatrix highOrder)
      Update the high order scaled derivatives Adams integrators (phase 2).

      The complete update of high order derivatives has a form similar to:

       rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn
       
      this method computes the (s1(n) - s1(n+1)) P-1 u part.

      Phase 1 of the update must already have been performed.

      Parameters:
      start - first order scaled derivatives at step start
      end - first order scaled derivatives at step end
      highOrder - high order scaled derivatives, will be modified (h2/2 y'', ... hk/k! y(k))
      See Also: