org.apache.commons.math3.ode.nonstiff

## Class LutherIntegrator

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

- All Implemented Interfaces:
    FirstOrderIntegrator, ODEIntegrator

      public class LutherIntegrator
      extends RungeKuttaIntegrator

  This class implements the Luther sixth order Runge-Kutta integrator for Ordinary Differential Equations.

  This method is described in H. A. Luther 1968 paper An explicit Sixth-Order Runge-Kutta Formula.

  This method is an explicit Runge-Kutta method, its Butcher-array is the following one :

              0   |               0                     0                     0                     0                     0                     0
              1   |               1                     0                     0                     0                     0                     0
             1/2  |              3/8                   1/8                    0                     0                     0                     0
             2/3  |              8/27                  2/27                  8/27                   0                     0                     0
         (7-q)/14 | (  -21 +   9q)/392    (  -56 +   8q)/392    (  336 -  48q)/392    (  -63 +   3q)/392                  0                     0
         (7+q)/14 | (-1155 - 255q)/1960   ( -280 -  40q)/1960   (    0 - 320q)/1960   (   63 + 363q)/1960   ( 2352 + 392q)/1960                 0
              1   | (  330 + 105q)/180    (  120 +   0q)/180    ( -200 + 280q)/180    (  126 - 189q)/180    ( -686 - 126q)/180     ( 490 -  70q)/180
                  |--------------------------------------------------------------------------------------------------------------------------------------------------
                  |              1/20                   0                   16/45                  0                   49/180                 49/180         1/20

  where q = √21
  Since:
    3.3
  See Also:
    `EulerIntegrator`, `ClassicalRungeKuttaIntegrator`, `GillIntegrator`, `MidpointIntegrator`, `ThreeEighthesIntegrator`

- - ### Field Summary

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

      `isLastStep, resetOccurred, stepHandlers, stepSize, stepStart`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `LutherIntegrator(double step)` Simple constructor.

  - ### Method Summary

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

      `integrate, singleStep`

    - ### 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

    - #### LutherIntegrator

          public LutherIntegrator(double step)

      Simple constructor. Build a fourth-order Luther integrator with the given step.
      Parameters:
        `step` - integration step

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