Package org.hipparchus.ode.nonstiff

Interface FieldExplicitRungeKuttaIntegrator<T extends CalculusFieldElement<T>>

Type Parameters:

T - the type of the field elements

All Superinterfaces:

FieldButcherArrayProvider<T>, FieldODEIntegrator<T>

All Known Implementing Classes:

ClassicalRungeKuttaFieldIntegrator, DormandPrince54FieldIntegrator, DormandPrince853FieldIntegrator, EmbeddedRungeKuttaFieldIntegrator, EulerFieldIntegrator, FixedStepRungeKuttaFieldIntegrator, GillFieldIntegrator, HighamHall54FieldIntegrator, LutherFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator

public interface FieldExplicitRungeKuttaIntegrator<T extends CalculusFieldElement<T>>
extends FieldButcherArrayProvider<T>, FieldODEIntegrator<T>

This interface implements the part of Runge-Kutta Field integrators for Ordinary Differential Equations common to fixed- and adaptive steps.

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:

3.1

See Also:

FieldButcherArrayProvider, FixedStepRungeKuttaFieldIntegrator, EmbeddedRungeKuttaFieldIntegrator

Method Summary

Modifier and Type	Method	Description
static <T extends CalculusFieldElement<T>> T[]	applyExternalButcherWeights(T[] y0, T[][] yDotK, T h, double[] b)	Apply external weights of Butcher array, assuming internal ones have been applied.
static <T extends CalculusFieldElement<T>> T[]	applyExternalButcherWeights(T[] y0, T[][] yDotK, T h, T[] b)	Apply external weights of Butcher array, assuming internal ones have been applied.
static <T extends CalculusFieldElement<T>> void	applyInternalButcherWeights(FieldExpandableODE<T> equations, T t0, T[] y0, T h, double[][] a, double[] c, T[][] yDotK)	Apply internal weights of Butcher array, with corresponding times.
static <T extends CalculusFieldElement<T>> void	applyInternalButcherWeights(FieldExpandableODE<T> equations, T t0, T[] y0, T h, T[][] a, T[] c, T[][] yDotK)	Apply internal weights of Butcher array, with corresponding times.
static <T extends CalculusFieldElement<T>> T	fraction(Field<T> field, double p, double q)	Create a fraction from doubles.
static <T extends CalculusFieldElement<T>> T	fraction(Field<T> field, int p, int q)	Create a fraction from integers.
default int	getNumberOfStages()	Getter for the number of stages corresponding to the Butcher array.
default double[][]	getRealA()	Get the internal weights from Butcher array (without the first empty row).
default double[]	getRealB()	Get the external weights for the high order method from Butcher array.
default double[]	getRealC()	Get the time steps from Butcher array (without the first zero).
boolean	isUsingFieldCoefficients()	Getter for the flag between real or Field coefficients in the Butcher array.
default T[]	singleStep(FieldOrdinaryDifferentialEquation<T> equations, T t0, T[] y0, T t)	Fast computation of a single step of ODE integration.

Methods inherited from interface org.hipparchus.ode.nonstiff.FieldButcherArrayProvider

getA, getB, getC

Methods inherited from interface org.hipparchus.ode.FieldODEIntegrator

addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, getCurrentSignedStepsize, getEvaluations, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepStart, integrate, setMaxEvaluations

Method Detail

getRealC

default double[] getRealC()

Get the time steps from Butcher array (without the first zero). Real version (non-Field).

Returns:

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

getRealA

default double[][] getRealA()

Get the internal weights from Butcher array (without the first empty row). Real version (non-Field).

Returns:

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

getRealB

default double[] getRealB()

Get the external weights for the high order method from Butcher array. Real version (non-Field).

Returns:

external weights for the high order method from Butcher array

isUsingFieldCoefficients

boolean isUsingFieldCoefficients()

Getter for the flag between real or Field coefficients in the Butcher array.

Returns:

flag

getNumberOfStages

default int getNumberOfStages()

Getter for the number of stages corresponding to the Butcher array.

Returns:

number of stages

singleStep

default T[] singleStep(FieldOrdinaryDifferentialEquation<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 FieldODEIntegrator.integrate(FieldExpandableODE, org.hipparchus.ode.FieldODEState, CalculusFieldElement) 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

fraction

static <T extends CalculusFieldElement<T>> T fraction(Field<T> field,
                                                      int p,
                                                      int q)

Create a fraction from integers.

Type Parameters:

T - the type of the field elements

Parameters:

field - field to which elements belong

p - numerator

q - denominator

Returns:

p/q computed in the instance field

fraction

static <T extends CalculusFieldElement<T>> T fraction(Field<T> field,
                                                      double p,
                                                      double q)

Create a fraction from doubles.

Type Parameters:

T - the type of the field elements

Parameters:

field - field to which elements belong

p - numerator

q - denominator

Returns:

p/q computed in the instance field

applyInternalButcherWeights

static <T extends CalculusFieldElement<T>> void applyInternalButcherWeights(FieldExpandableODE<T> equations,
                                                                            T t0,
                                                                            T[] y0,
                                                                            T h,
                                                                            T[][] a,
                                                                            T[] c,
                                                                            T[][] yDotK)

Apply internal weights of Butcher array, with corresponding times.

Type Parameters:

T - the type of the field elements

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

h - step size

a - internal weights of Butcher array

c - times of Butcher array

yDotK - array where to store result

applyInternalButcherWeights

static <T extends CalculusFieldElement<T>> void applyInternalButcherWeights(FieldExpandableODE<T> equations,
                                                                            T t0,
                                                                            T[] y0,
                                                                            T h,
                                                                            double[][] a,
                                                                            double[] c,
                                                                            T[][] yDotK)

Apply internal weights of Butcher array, with corresponding times. Version with real Butcher array (non-Field).

Type Parameters:

T - the type of the field elements

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

h - step size

a - internal weights of Butcher array

c - times of Butcher array

yDotK - array where to store result

applyExternalButcherWeights

static <T extends CalculusFieldElement<T>> T[] applyExternalButcherWeights(T[] y0,
                                                                           T[][] yDotK,
                                                                           T h,
                                                                           T[] b)

Apply external weights of Butcher array, assuming internal ones have been applied.

Type Parameters:

T - the type of the field elements

Parameters:

yDotK - output of stages

y0 - initial value of the state vector at t0

h - step size

b - external weights of Butcher array

Returns:

state vector

applyExternalButcherWeights

static <T extends CalculusFieldElement<T>> T[] applyExternalButcherWeights(T[] y0,
                                                                           T[][] yDotK,
                                                                           T h,
                                                                           double[] b)

Apply external weights of Butcher array, assuming internal ones have been applied. Version with real Butcher array (non-Field version).

Type Parameters:

T - the type of the field elements

Parameters:

yDotK - output of stages

y0 - initial value of the state vector at t0

h - step size

b - external weights of Butcher array

Returns:

state vector