Package org.hipparchus.ode.nonstiff

Class EulerIntegrator

java.lang.Object

org.hipparchus.ode.AbstractIntegrator

org.hipparchus.ode.nonstiff.RungeKuttaIntegrator

org.hipparchus.ode.nonstiff.EulerIntegrator

All Implemented Interfaces:

ButcherArrayProvider, ExplicitRungeKuttaIntegrator, ODEIntegrator

public class EulerIntegrator
extends RungeKuttaIntegrator

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:

• MidpointIntegrator
• ClassicalRungeKuttaIntegrator
• GillIntegrator
• ThreeEighthesIntegrator
• LutherIntegrator

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor	Description
EulerIntegrator(double step)	Simple constructor.

Method Summary

Modifier and Type	Method	Description
protected org.hipparchus.ode.nonstiff.EulerStateInterpolator	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

EulerIntegrator

public EulerIntegrator(double step)

Simple constructor. Build an Euler 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.EulerStateInterpolator 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