Package org.hipparchus.ode.nonstiff

Class LutherIntegrator

java.lang.Object

org.hipparchus.ode.AbstractIntegrator

org.hipparchus.ode.nonstiff.RungeKuttaIntegrator

org.hipparchus.ode.nonstiff.LutherIntegrator

All Implemented Interfaces:

ButcherArrayProvider, ExplicitRungeKuttaIntegrator, 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

See Also:

• EulerIntegrator
• ClassicalRungeKuttaIntegrator
• GillIntegrator
• MidpointIntegrator
• ThreeEighthesIntegrator

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor	Description
LutherIntegrator(double step)	Simple constructor.

Method Summary

Modifier and Type	Method	Description
protected org.hipparchus.ode.nonstiff.LutherStateInterpolator	createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper)	Create an interpolator.
double[][]	getA()	Get the internal weights from Butcher array (without the first empty row).
double[]	getB()	Get the external weights for the high order method from Butcher array.
double[]	getC()	Get the time steps from Butcher array (without the first zero).

Methods inherited from class org.hipparchus.ode.nonstiff.RungeKuttaIntegrator

getDefaultStep, integrate

Methods inherited from class org.hipparchus.ode.AbstractIntegrator

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

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

getNumberOfStages, singleStep

Methods inherited from interface org.hipparchus.ode.ODEIntegrator

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

Field Details

METHOD_NAME

public static final String METHOD_NAME

Name of integration scheme.

See Also:

• Constant Field Values

Constructor Details

LutherIntegrator

public LutherIntegrator(double step)

Simple constructor. Build a fourth-order Luther integrator with the given step.

Parameters:

step - integration step

Method Details

getC

public double[] getC()

Get the time steps from Butcher array (without the first zero).

Returns:

time steps from Butcher array (without the first zero

getA

public double[][] 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 double[] 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.LutherStateInterpolator createInterpolator(boolean forward,
 double[][] yDotK,
 ODEStateAndDerivative globalPreviousState,
 ODEStateAndDerivative globalCurrentState,
 EquationsMapper mapper)

Create an interpolator.

Specified by:

createInterpolator in class RungeKuttaIntegrator

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