Package org.hipparchus.ode.nonstiff

Class LutherFieldIntegrator<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.ode.AbstractFieldIntegrator<T>

org.hipparchus.ode.nonstiff.RungeKuttaFieldIntegrator<T>

org.hipparchus.ode.nonstiff.LutherFieldIntegrator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FieldODEIntegrator<T>, FieldButcherArrayProvider<T>, FieldExplicitRungeKuttaIntegrator<T>

public class LutherFieldIntegrator<T extends CalculusFieldElement<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

See Also:

• EulerFieldIntegrator
• ClassicalRungeKuttaFieldIntegrator
• GillFieldIntegrator
• MidpointFieldIntegrator
• ThreeEighthesFieldIntegrator

Field Summary

Fields

Modifier and Type	Field	Description
static final String	METHOD_NAME	Name of integration scheme.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
protected org.hipparchus.ode.nonstiff.LutherFieldStateInterpolator<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.hipparchus.ode.nonstiff.RungeKuttaFieldIntegrator

getDefaultStep, getNumberOfStages, initIntegration, integrate, isUsingFieldCoefficients, setUsingFieldCoefficients

Methods inherited from class org.hipparchus.ode.AbstractFieldIntegrator

acceptStep, addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEquations, getEvaluations, getEvaluationsCounter, getEventDetectors, getField, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepSize, getStepStart, incrementEvaluations, 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

Methods inherited from interface org.hipparchus.ode.nonstiff.FieldExplicitRungeKuttaIntegrator

getRealA, getRealB, getRealC, singleStep

Methods inherited from interface org.hipparchus.ode.FieldODEIntegrator

addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, getCurrentSignedStepsize, getEvaluations, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepStart, setMaxEvaluations

Field Details

METHOD_NAME

public static final String METHOD_NAME

Name of integration scheme.

See Also:

• Constant Field Values

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 org.hipparchus.ode.nonstiff.LutherFieldStateInterpolator<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 CalculusFieldElement<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