Package org.hipparchus.ode.nonstiff

Class EulerFieldIntegrator<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.ode.AbstractFieldIntegrator<T>

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

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

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

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

public class EulerFieldIntegrator<T extends CalculusFieldElement<T>>
extends RungeKuttaFieldIntegrator<T>

This class implements a simple Euler integrator for Ordinary Differential Equations.

The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.

See Also:

• MidpointFieldIntegrator
• ClassicalRungeKuttaFieldIntegrator
• GillFieldIntegrator
• ThreeEighthesFieldIntegrator
• LutherFieldIntegrator

Field Summary

Fields

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

Constructor Summary

Constructors

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

Method Summary

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

EulerFieldIntegrator

public EulerFieldIntegrator(Field<T> field,
 T step)

Simple constructor. Build an Euler 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.EulerFieldStateInterpolator<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