Package org.hipparchus.ode.nonstiff

Class EmbeddedRungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>>

java.lang.Object
org.hipparchus.ode.AbstractFieldIntegrator<T>
org.hipparchus.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>
org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaFieldIntegrator<T>
Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
FieldODEIntegrator<T>, FieldButcherArrayProvider<T>, FieldExplicitRungeKuttaIntegrator<T>
Direct Known Subclasses:
DormandPrince54FieldIntegrator, DormandPrince853FieldIntegrator, HighamHall54FieldIntegrator
public abstract class EmbeddedRungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>> extends AdaptiveStepsizeFieldIntegrator<T> implements FieldExplicitRungeKuttaIntegrator<T>
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

    • EmbeddedRungeKuttaFieldIntegrator

      protected EmbeddedRungeKuttaFieldIntegrator(Field<T> field, String name, int fsal, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
      Build a Runge-Kutta integrator with the given Butcher array.
      Parameters:
      field - field to which the time and state vector elements belong
      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

    • EmbeddedRungeKuttaFieldIntegrator

      protected EmbeddedRungeKuttaFieldIntegrator(Field<T> field, String name, int fsal, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
      Build a Runge-Kutta integrator with the given Butcher array.
      Parameters:
      field - field to which the time and state vector elements belong
      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.RungeKuttaFieldStateInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> 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 T getSafety()
      Get the safety factor for stepsize control.
      Returns:
      safety factor

    • setSafety

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

    • setUsingFieldCoefficients

      public void setUsingFieldCoefficients(boolean usingFieldCoefficients)
      Setter for the flag between real or Field coefficients in the Butcher array.
      Parameters:
      usingFieldCoefficients - new value for flag

    • isUsingFieldCoefficients

      public boolean isUsingFieldCoefficients()
      Getter for the flag between real or Field coefficients in the Butcher array.
      Specified by:
      isUsingFieldCoefficients in interface FieldExplicitRungeKuttaIntegrator<T extends CalculusFieldElement<T>>
      Returns:
      flag

    • getNumberOfStages

      public int getNumberOfStages()
      Getter for the number of stages corresponding to the Butcher array.
      Specified by:
      getNumberOfStages in interface FieldExplicitRungeKuttaIntegrator<T extends CalculusFieldElement<T>>
      Returns:
      number of stages

    • initIntegration

      protected FieldODEStateAndDerivative<T> initIntegration(FieldExpandableODE<T> eqn, FieldODEState<T> s0, T t)
      Prepare the start of an integration.
      Overrides:
      initIntegration in class AbstractFieldIntegrator<T extends CalculusFieldElement<T>>
      Parameters:
      eqn - equations to integrate
      s0 - initial state vector
      t - target time for the integration
      Returns:
      initial state with derivatives added

    • integrate

      public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T 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 (FieldODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

      Specified by:
      integrate in interface FieldODEIntegrator<T extends CalculusFieldElement<T>>
      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 FieldODEEventHandler stops it at some point.
      Throws:
      MathIllegalArgumentException - if integration step is too small
      MathIllegalStateException - if the number of functions evaluations is exceeded

    • getMinReduction

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

    • setMinReduction

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

    • getMaxGrowth

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

    • setMaxGrowth

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

    • estimateError

      protected abstract double estimateError(T[][] yDotK, T[] y0, T[] y1, T 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