Class LutherFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object
org.apache.commons.math3.ode.AbstractFieldIntegrator<T>
org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator<T>
org.apache.commons.math3.ode.nonstiff.LutherFieldIntegrator<T>
Type Parameters:
T - the type of the field elements
All Implemented Interfaces:
FirstOrderFieldIntegrator<T>, FieldButcherArrayProvider<T>
public class LutherFieldIntegrator<T extends RealFieldElement<T>> extends RungeKuttaFieldIntegrator<T>
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:
3.6
See Also:

  • Constructor Details

    • LutherFieldIntegrator

      public LutherFieldIntegrator(Field<T> field, T step)
      Simple constructor. Build a fourth-order Luther integrator with the given step.
      Parameters:
      field - field to which the time and state vector elements belong
      step - integration step

  • Method Details

    • getC

      public T[] getC()
      Get the time steps from Butcher array (without the first zero).
      Returns:
      time steps from Butcher array (without the first zero

    • getA

      public T[][] getA()
      Get the internal weights from Butcher array (without the first empty row).
      Returns:
      internal weights from Butcher array (without the first empty row)

    • getB

      public T[] getB()
      Get the external weights for the high order method from Butcher array.
      Returns:
      external weights for the high order method from Butcher array

    • createInterpolator

      protected LutherFieldStepInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)
      Create an interpolator.
      Specified by:
      createInterpolator in class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
      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