Package org.apache.commons.math3.ode.nonstiff

Class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object
org.apache.commons.math3.ode.AbstractFieldIntegrator<T>
org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator<T>
Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
FirstOrderFieldIntegrator<T>, FieldButcherArrayProvider<T>
Direct Known Subclasses:
ClassicalRungeKuttaFieldIntegrator, EulerFieldIntegrator, GillFieldIntegrator, LutherFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator
public abstract class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>> extends AbstractFieldIntegrator<T> implements FieldButcherArrayProvider<T>
This class implements the common part of all fixed step Runge-Kutta integrators for Ordinary Differential Equations.

These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows : 

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

Since:
3.6
See Also:

  • Constructor Details

    • RungeKuttaFieldIntegrator

      protected RungeKuttaFieldIntegrator(Field<T> field, String name, T step)
      Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing.
      Parameters:
      field - field to which the time and state vector elements belong
      name - name of the method
      step - integration step

  • Method Details

    • fraction

      protected T fraction(int p, int q)
      Create a fraction.
      Parameters:
      p - numerator
      q - denominator
      Returns:
      p/q computed in the instance field

    • createInterpolator

      protected abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<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

    • integrate

      public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime) throws NumberIsTooSmallException, DimensionMismatchException, MaxCountExceededException, NoBracketingException
      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 (FirstOrderFieldIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

      Specified by:
      integrate in interface FirstOrderFieldIntegrator<T extends RealFieldElement<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 FieldEventHandler stops it at some point.
      Throws:
      NumberIsTooSmallException - if integration step is too small
      MaxCountExceededException - if the number of functions evaluations is exceeded
      NoBracketingException - if the location of an event cannot be bracketed
      DimensionMismatchException

    • singleStep

      public T[] singleStep(FirstOrderFieldDifferentialEquations<T> equations, T t0, T[] y0, T t)
      Fast computation of a single step of ODE integration.

      This method is intended for the limited use case of very fast computation of only one step without using any of the rich features of general integrators that may take some time to set up (i.e. no step handlers, no events handlers, no additional states, no interpolators, no error control, no evaluations count, no sanity checks ...). It handles the strict minimum of computation, so it can be embedded in outer loops.

      This method is not used at all by the integrate(FieldExpandableODE, FieldODEState, RealFieldElement) method. It also completely ignores the step set at construction time, and uses only a single step to go from t0 to t.

      As this method does not use any of the state-dependent features of the integrator, it should be reasonably thread-safe if and only if the provided differential equations are themselves thread-safe.

      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)
      Returns:
      state vector at t