Module: svIntegratorRungeKutta

template<size_t numberStages>
struct RKCoefficients

#include <svIntegratorRungeKutta.h>

Stores the coefficients necessary to use the Runge-Kutta methods.

The Butcher table looks like:

c | A

b

Subclassed by RKAdaptiveCoefficients< numberStages >

Public Types

using StageSizedArray = std::array<double, numberStages>

Array with size = numberStages

using StageSizedMatrix = std::array<StageSizedArray, numberStages>

Square matrix with size = numberStages

Public Members

StageSizedMatrix aMatrix = {}

“a” coefficient matrix of the RK method

StageSizedArray bArray = {}

“b” coefficient array of the RK method

StageSizedArray cArray = {}

“c” coefficient array of the RK method

template<size_t numberStages>
class svIntegratorRungeKutta : public StateVecIntegrator

#include <svIntegratorRungeKutta.h>

The svIntegratorRungeKutta class implements a state integrator based on the family of explicit Runge-Kutta numerical integrators.

A Runge-Kutta method is defined by its stage number and its coefficients. The stage number drives the computational cost of the method: an RK method of stage 4 requires 4 dynamics evaluations (FSAL optimizations are not done).

Note that the order of the integrator is lower or equal to the stage number. A RK method of order 5, for example, requires 7 stages.

Subclassed by svIntegratorAdaptiveRungeKutta< numberStages >

Public Functions

svIntegratorRungeKutta(DynamicObject *dynIn, const RKCoefficients<numberStages> &coefficients)

Creates an explicit RK integrator for the given DynamicObject using the passed coefficients.

virtual void integrate(double currentTime, double timeStep) override

Performs the integration of the associated dynamic objects up to time currentTime+timeStep

Protected Types

using KCoefficientsValues = std::array<ExtendedStateVector, numberStages>

For an s-stage RK method, s number of “k” coefficients are needed, where each “k” coefficient has the same size as the state. This type allows us to store these “k” coefficients.

Protected Functions

svIntegratorRungeKutta(DynamicObject *dynIn, std::unique_ptr<RKCoefficients<numberStages>> &&coefficients)

Can be used by subclasses to support passing coefficients that are subclasses of RKCoefficients

ExtendedStateVector computeDerivatives(double time, double timeStep, const ExtendedStateVector &states)

Computes the derivatives of every state given a time and current states.

Internally, this sets the states on the dynamic objects and calls the equationsOfMotion methods.

KCoefficientsValues computeKCoefficients(double currentTime, double timeStep, const ExtendedStateVector &currentStates)

Computes the “k” coefficients of the Runge-Kutta method for a time and state.

ExtendedStateVector propagateStateWithKVectors(double timeStep, const ExtendedStateVector &currentStates, const KCoefficientsValues &kVectors, const std::array<double, numberStages> &coefficients, size_t maxStage)

Computes:

 y = y_0 + dt*( coeff_0*k_0 + coeff_1*k_1 + ... + coeff_maxStage*k_maxStage )

where y_0 is currentStates, dt is timeStep, [coeff_0, coeff_1, …] is coefficients and [k_0, k_1, …] is kVectors.

Protected Attributes

const std::unique_ptr<RKCoefficients<numberStages>> coefficients

Coefficients to be used in the method