Package org.apache.commons.math4.legacy.ode.nonstiff

Class LutherFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator<T>

org.apache.commons.math4.legacy.ode.nonstiff.RungeKuttaFieldIntegrator<T>

org.apache.commons.math4.legacy.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:

EulerFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator

Constructor Summary

Constructors

Constructor	Description
LutherFieldIntegrator(Field<T> field, T step)	Simple constructor.

Method Summary

Modifier and Type	Method	Description
protected org.apache.commons.math4.legacy.ode.nonstiff.LutherFieldStepInterpolator<T>	createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)	Create an interpolator.
T[][]	getA()	Get the internal weights from Butcher array (without the first empty row).
T[]	getB()	Get the external weights for the high order method from Butcher array.
T[]	getC()	Get the time steps from Butcher array (without the first zero).

Methods inherited from class org.apache.commons.math4.legacy.ode.nonstiff.RungeKuttaFieldIntegrator

fraction, integrate, singleStep

Methods inherited from class org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getField, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, initIntegration, isLastStep, resetOccurred, sanityChecks, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStart

Methods inherited from class java.lang.Object

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

Constructor Detail

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 Detail

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 org.apache.commons.math4.legacy.ode.nonstiff.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