Package org.apache.commons.math4.legacy.ode.nonstiff

Class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator<T>

org.apache.commons.math4.legacy.ode.nonstiff.RungeKuttaFieldIntegrator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FirstOrderFieldIntegrator<T>, FieldButcherArrayProvider<T>

Direct Known Subclasses:

ClassicalRungeKuttaFieldIntegrator, EulerFieldIntegrator, GillFieldIntegrator, LutherFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator

public abstract class RungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
extends AbstractFieldIntegrator<T>
implements FieldButcherArrayProvider<T>

This class implements the common part of all fixed step Runge-Kutta integrators for Ordinary Differential Equations.

These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
 

Since:

3.6

See Also:

EulerFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, MidpointFieldIntegrator

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	RungeKuttaFieldIntegrator(Field<T> field, String name, T step)	Simple constructor.

Method Summary

Modifier and Type	Method	Description
protected abstract org.apache.commons.math4.legacy.ode.nonstiff.RungeKuttaFieldStepInterpolator<T>	createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)	Create an interpolator.
protected T	fraction(int p, int q)	Create a fraction.
FieldODEStateAndDerivative<T>	integrate(FieldExpandableODE<T> equations, FieldODEState<T> initialState, T finalTime)	Integrate the differential equations up to the given time.
T[]	singleStep(FirstOrderFieldDifferentialEquations<T> equations, T t0, T[] y0, T t)	Fast computation of a single step of ODE integration.

Methods inherited from class org.apache.commons.math4.legacy.ode.AbstractFieldIntegrator

acceptStep, 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, setStepStart

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.math4.legacy.ode.nonstiff.FieldButcherArrayProvider

getA, getB, getC

Constructor Detail

RungeKuttaFieldIntegrator

protected RungeKuttaFieldIntegrator(Field<T> field,
                                    String name,
                                    T step)

Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing.

Parameters:

field - field to which the time and state vector elements belong

name - name of the method

step - integration step

Method Detail

fraction

protected T fraction(int p,
                     int q)

Create a fraction.

Parameters:

p - numerator

q - denominator

Returns:

p/q computed in the instance field

createInterpolator

protected abstract org.apache.commons.math4.legacy.ode.nonstiff.RungeKuttaFieldStepInterpolator<T> createInterpolator(boolean forward,
                                                                                                                      T[][] yDotK,
                                                                                                                      FieldODEStateAndDerivative<T> globalPreviousState,
                                                                                                                      FieldODEStateAndDerivative<T> globalCurrentState,
                                                                                                                      FieldEquationsMapper<T> mapper)

Create an interpolator.

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

integrate

public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE<T> equations,
                                               FieldODEState<T> initialState,
                                               T finalTime)
                                        throws NumberIsTooSmallException,
                                               DimensionMismatchException,
                                               MaxCountExceededException,
                                               NoBracketingException

Integrate the differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

Since this method stores some internal state variables made available in its public interface during integration (FirstOrderFieldIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Specified by:

integrate in interface FirstOrderFieldIntegrator<T extends RealFieldElement<T>>

Parameters:

equations - differential equations to integrate

initialState - initial state (time, primary and secondary state vectors)

finalTime - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

final state, its time will be the same as finalTime if integration reached its target, but may be different if some FieldEventHandler stops it at some point.

Throws:

NumberIsTooSmallException - if integration step is too small

MaxCountExceededException - if the number of functions evaluations is exceeded

NoBracketingException - if the location of an event cannot be bracketed

DimensionMismatchException

singleStep

public T[] singleStep(FirstOrderFieldDifferentialEquations<T> equations,
                      T t0,
                      T[] y0,
                      T t)

Fast computation of a single step of ODE integration.

This method is intended for the limited use case of very fast computation of only one step without using any of the rich features of general integrators that may take some time to set up (i.e. no step handlers, no events handlers, no additional states, no interpolators, no error control, no evaluations count, no sanity checks ...). It handles the strict minimum of computation, so it can be embedded in outer loops.

This method is not used at all by the integrate(FieldExpandableODE, FieldODEState, RealFieldElement) method. It also completely ignores the step set at construction time, and uses only a single step to go from t0 to t.

As this method does not use any of the state-dependent features of the integrator, it should be reasonably thread-safe if and only if the provided differential equations are themselves thread-safe.

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

t - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

state vector at t