T - the type of the field elementspublic class EulerFieldIntegrator<T extends RealFieldElement<T>> extends RungeKuttaFieldIntegrator<T>
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.
| Constructor and Description |
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EulerFieldIntegrator(Field<T> field,
T step)
Simple constructor.
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| Modifier and Type | Method and Description |
|---|---|
protected org.apache.commons.math3.ode.nonstiff.EulerFieldStepInterpolator<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).
|
fraction, integrate, singleStepacceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getField, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, initIntegration, isLastStep, resetOccurred, sanityChecks, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStartpublic T[] getC()
public T[][] getA()
public T[] getB()
protected org.apache.commons.math3.ode.nonstiff.EulerFieldStepInterpolator<T> createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)
createInterpolator in class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>forward - integration direction indicatoryDotK - slopes at the intermediate pointsglobalPreviousState - start of the global stepglobalCurrentState - end of the global stepmapper - equations mapper for the all equationsCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.