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

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

addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, integrate, setMaxEvaluations

Methods inherited from class java.lang.Object

equals, 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