Top Description Constructors Methods
org.apache.commons.math3.ode.nonstiff

public Class EulerFieldIntegrator<T extends RealFieldElement<T>>

extends RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
Class Inheritance
Type Parameters
<T>
the type of the field elements
Imports
org.apache.commons.math3.Field, .RealFieldElement, org.apache.commons.math3.ode.FieldEquationsMapper, .FieldODEStateAndDerivative, org.apache.commons.math3.util.MathArrays

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.

Since
3.6
See Also
MidpointFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, ThreeEighthesFieldIntegrator, LutherFieldIntegrator

Constructor Summary

AccessConstructor and Description
public
EulerFieldIntegrator(final Field<T>
field to which the time and state vector elements belong
field
,
final T
integration step
step
)

Simple constructor.

Method Summary

Modifier and TypeMethod and Description
protected EulerFieldStepInterpolator<T>
createInterpolator(final boolean
integration direction indicator
forward
,
T[][]
slopes at the intermediate points
yDotK
,
final FieldODEStateAndDerivative<T>
start of the global step
globalPreviousState
,
final FieldODEStateAndDerivative<T>
end of the global step
globalCurrentState
,
final FieldEquationsMapper<T>
equations mapper for the all equations
mapper
)

Implements abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator.createInterpolator.

Create an interpolator.

public T[][]
getA()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getA.

Get the internal weights from Butcher array (without the first empty row).

public T[]
getB()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getB.

Get the external weights for the high order method from Butcher array.

public T[]
getC()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getC.

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

Inherited from org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator:
fractionintegratesingleStep

Constructor Detail

EulerFieldIntegratorback to summary
public EulerFieldIntegrator(final Field<T> field, final T step)

Simple constructor. Build an Euler integrator with the given step.

Parameters
field:Field<T>

field to which the time and state vector elements belong

step:T

integration step

Method Detail

createInterpolatorback to summary
protected EulerFieldStepInterpolator<T> createInterpolator(final boolean forward, T[][] yDotK, final FieldODEStateAndDerivative<T> globalPreviousState, final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper)

Implements abstract org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator.createInterpolator.

Doc from org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldIntegrator.createInterpolator.

Create an interpolator.

Parameters
forward:boolean

integration direction indicator

yDotK:T[][]

slopes at the intermediate points

globalPreviousState:FieldODEStateAndDerivative<T>

start of the global step

globalCurrentState:FieldODEStateAndDerivative<T>

end of the global step

mapper:FieldEquationsMapper<T>

equations mapper for the all equations

Returns:EulerFieldStepInterpolator<T>

external weights for the high order method from Butcher array

Annotations
@Override
getAback to summary
public T[][] getA()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getA.

Doc from org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getA.

Get the internal weights from Butcher array (without the first empty row).

Returns:T[][]

internal weights from Butcher array (without the first empty row)

getBback to summary
public T[] getB()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getB.

Doc from org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getB.

Get the external weights for the high order method from Butcher array.

Returns:T[]

external weights for the high order method from Butcher array

getCback to summary
public T[] getC()

Implements org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getC.

Doc from org.apache.commons.math3.ode.nonstiff.FieldButcherArrayProvider.getC.

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

Returns:T[]

time steps from Butcher array (without the first zero