org.apache.commons.math3.ode.nonstiff

## Class RungeKuttaIntegrator

- java.lang.Object
- - org.apache.commons.math3.ode.AbstractIntegrator
  - - org.apache.commons.math3.ode.nonstiff.RungeKuttaIntegrator

- All Implemented Interfaces:
    FirstOrderIntegrator, ODEIntegrator
  Direct Known Subclasses:
    ClassicalRungeKuttaIntegrator, EulerIntegrator, GillIntegrator, LutherIntegrator, MidpointIntegrator, ThreeEighthesIntegrator

      public abstract class RungeKuttaIntegrator
      extends AbstractIntegrator

  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:
    1.2
  See Also:
    `EulerIntegrator`, `ClassicalRungeKuttaIntegrator`, `GillIntegrator`, `MidpointIntegrator`

- - ### Field Summary

    - ### Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator

      `isLastStep, resetOccurred, stepHandlers, stepSize, stepStart`

  - ### Constructor Summary

    Constructors
    Modifier | Constructor and Description
    --- | ---
    `protected` | `RungeKuttaIntegrator(String name, double[] c, double[][] a, double[] b, org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype, double step)` Simple constructor.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `void` | `integrate(ExpandableStatefulODE equations, double t)` Integrate a set of differential equations up to the given time.
    `double[]` | `singleStep(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t)` Fast computation of a single step of ODE integration.

    - ### Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

      `acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCounter, getCurrentSignedStepsize, getCurrentStepStart, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, sanityChecks, setEquations, setMaxEvaluations, setStateInitialized`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### RungeKuttaIntegrator

          protected RungeKuttaIntegrator(String name,
                              double[] c,
                              double[][] a,
                              double[] b,
                              org.apache.commons.math3.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                              double step)

      Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing.
      Parameters:
        `name` - name of the method
        `c` - time steps from Butcher array (without the first zero)
        `a` - internal weights from Butcher array (without the first empty row)
        `b` - propagation weights for the high order method from Butcher array
        `prototype` - prototype of the step interpolator to use
        `step` - integration step

  - ### Method Detail

    - #### integrate

          public void integrate(ExpandableStatefulODE equations,
                       double t)
                         throws NumberIsTooSmallException,
                                DimensionMismatchException,
                                MaxCountExceededException,
                                NoBracketingException

      Integrate a set of differential equations up to the given time.

      This method solves an Initial Value Problem (IVP).

      The set of differential equations is composed of a main set, which can be extended by some sets of secondary equations. The set of equations must be already set up with initial time and partial states. At integration completion, the final time and partial states will be available in the same object.

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

      Specified by:
        `integrate` in class `AbstractIntegrator`
      Parameters:
        `equations` - complete set of differential equations to integrate
        `t` - target time for the integration (can be set to a value smaller than `t0` for backward integration)
      Throws:
        `NumberIsTooSmallException` - if integration step is too small
        `DimensionMismatchException` - if the dimension of the complete state does not match the complete equations sets dimension
        `MaxCountExceededException` - if the number of functions evaluations is exceeded
        `NoBracketingException` - if the location of an event cannot be bracketed

    - #### singleStep

          public double[] singleStep(FirstOrderDifferentialEquations equations,
                            double t0,
                            double[] y0,
                            double 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(ExpandableStatefulODE, double)` 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`

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