Package org.hipparchus.ode.nonstiff

Class EmbeddedRungeKuttaIntegrator

java.lang.Object
org.hipparchus.ode.AbstractIntegrator
org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator
org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaIntegrator
All Implemented Interfaces:
ButcherArrayProvider, ExplicitRungeKuttaIntegrator, ODEIntegrator
Direct Known Subclasses:
DormandPrince54Integrator, DormandPrince853Integrator, HighamHall54Integrator
public abstract class EmbeddedRungeKuttaIntegrator extends AdaptiveStepsizeIntegrator implements ExplicitRungeKuttaIntegrator
This class implements the common part of all embedded Runge-Kutta integrators for Ordinary Differential Equations.

These methods are embedded explicit Runge-Kutta methods with two sets of coefficients allowing to estimate the error, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
       |  b'1  b'2 ...   b's-1 b's

In fact, we rather use the array defined by ej = bj - b'j to compute directly the error rather than computing two estimates and then comparing them.

Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.

  • Constructor Details

    • EmbeddedRungeKuttaIntegrator

      protected EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
      Build a Runge-Kutta integrator with the given Butcher array.
      Parameters:
      name - name of the method
      fsal - index of the pre-computed derivative for fsal methods or -1 if method is not fsal
      minStep - minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      scalAbsoluteTolerance - allowed absolute error
      scalRelativeTolerance - allowed relative error

    • EmbeddedRungeKuttaIntegrator

      protected EmbeddedRungeKuttaIntegrator(String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
      Build a Runge-Kutta integrator with the given Butcher array.
      Parameters:
      name - name of the method
      fsal - index of the pre-computed derivative for fsal methods or -1 if method is not fsal
      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

  • Method Details

    • createInterpolator

      protected abstract org.hipparchus.ode.nonstiff.RungeKuttaStateInterpolator createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper)
      Create an interpolator.
      Parameters:
      forward - integration direction indicator
      yDotK - slopes at the intermediate points
      globalPreviousState - start of the global step
      globalCurrentState - end of the global step
      mapper - equations mapper for the all equations
      Returns:
      external weights for the high order method from Butcher array

    • getOrder

      public abstract int getOrder()
      Get the order of the method.
      Returns:
      order of the method

    • getSafety

      public double getSafety()
      Get the safety factor for stepsize control.
      Returns:
      safety factor

    • setSafety

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

    • integrate

      public ODEStateAndDerivative integrate(ExpandableODE equations, ODEState initialState, double finalTime) throws MathIllegalArgumentException, MathIllegalStateException
      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 ODEIntegrator
      Parameters:
      equations - differential equations to integrate
      initialState - initial state (time, primary and secondary state vectors)
      finalTime - target time for the integration (can be set to a value smaller than t0 for backward integration)
      Returns:
      final state, its time will be the same as finalTime if integration reached its target, but may be different if some ODEEventHandler stops it at some point.
      Throws:
      MathIllegalArgumentException - if integration step is too small
      MathIllegalStateException - if the number of functions evaluations is exceeded

    • getMinReduction

      public double getMinReduction()
      Get the minimal reduction factor for stepsize control.
      Returns:
      minimal reduction factor

    • setMinReduction

      public void setMinReduction(double minReduction)
      Set the minimal reduction factor for stepsize control.
      Parameters:
      minReduction - minimal reduction factor

    • getMaxGrowth

      public double getMaxGrowth()
      Get the maximal growth factor for stepsize control.
      Returns:
      maximal growth factor

    • setMaxGrowth

      public void setMaxGrowth(double maxGrowth)
      Set the maximal growth factor for stepsize control.
      Parameters:
      maxGrowth - maximal growth factor

    • estimateError

      protected abstract double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
      Compute the error ratio.
      Parameters:
      yDotK - derivatives computed during the first stages
      y0 - estimate of the step at the start of the step
      y1 - estimate of the step at the end of the step
      h - current step
      Returns:
      error ratio, greater than 1 if step should be rejected