TimeSteppers::ClassicalRungeKutta4 Class Reference

#include <ClassicalRungeKutta4.hpp>

Public Types
using	options = tmpl::list<>
Public Types inherited from TimeStepper
using	provided_time_stepper_interfaces = tmpl::list<TimeStepper>

Public Member Functions
	ClassicalRungeKutta4 (const ClassicalRungeKutta4 &)=default
ClassicalRungeKutta4 &	operator= (const ClassicalRungeKutta4 &)=default
	ClassicalRungeKutta4 (ClassicalRungeKutta4 &&)=default
ClassicalRungeKutta4 &	operator= (ClassicalRungeKutta4 &&)=default
variants::TaggedVariant< Tags::FixedOrder, Tags::VariableOrder >	order () const override
	The convergence order of the stepper.
double	stable_step () const override
	Rough estimate of the maximum step size this method can take stably as a multiple of the step for Euler's method.
	WRAPPED_PUPable_decl_template (ClassicalRungeKutta4)
	ClassicalRungeKutta4 (CkMigrateMessage *)
const ButcherTableau &	butcher_tableau () const override
Public Member Functions inherited from TimeSteppers::RungeKutta
uint64_t	number_of_substeps () const override
	Number of substeps in this TimeStepper.
uint64_t	number_of_substeps_for_error () const override
	Number of substeps in this TimeStepper when providing an error measure for adaptive time-stepping.
size_t	number_of_past_steps () const override
	Number of past time steps needed for multi-step method.
bool	monotonic () const override
	Whether computational and temporal orderings of operations match.
TimeStepId	next_time_id (const TimeStepId &current_id, const TimeDelta &time_step) const override
	The TimeStepId after the current substep.
TimeStepId	next_time_id_for_error (const TimeStepId &current_id, const TimeDelta &time_step) const override
	The TimeStepId after the current substep when providing an error measure for adaptive time-stepping.
Public Member Functions inherited from TimeStepper
	WRAPPED_PUPable_abstract (TimeStepper)
template<typename Vars>
void	update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const TimeDelta &time_step) const
	Set u to the value at the end of the current substep.
template<typename Vars>
std::optional< StepperErrorEstimate >	update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const TimeDelta &time_step, const StepperErrorTolerances &tolerances) const
	Set u to the value at the end of the current substep; report the error measure when available.
template<typename Vars>
void	clean_history (const gsl::not_null< TimeSteppers::History< Vars > * > history) const
	Remove old entries from the history.
template<typename Vars>
bool	dense_update_u (const gsl::not_null< Vars * > u, const TimeSteppers::History< Vars > &history, const double time) const
	Compute the solution value at a time between steps. To evaluate at a time within a given step, call this method at the start of the step containing the time. The function returns true on success, otherwise the call should be retried after the next substep.
template<typename Vars>
bool	can_change_step_size (const TimeStepId &time_id, const TimeSteppers::History< Vars > &history) const
	Whether a change in the step size is allowed before taking a step. Step sizes can never be changed on a substep.

Static Public Attributes
static constexpr Options::String	help
Static Public Attributes inherited from TimeStepper
static constexpr bool	local_time_stepping = false
static constexpr bool	imex = false

Detailed Description

The standard 4th-order Runge-Kutta method, given e.g. in https://en.wikipedia.org/wiki/Runge-Kutta_methods that solves equations of the form

\begin{eqnarray}\frac{du}{dt} & = & \mathcal{L}(t,u). \end{eqnarray}

Given a solution \(u(t^n)=u^n\), this stepper computes \(u(t^{n+1})=u^{n+1}\) using the following equations:

\begin{eqnarray}v^{(1)} & = & u^n + dt\cdot \mathcal{L}(t^n, u^n)/2,\\ v^{(2)} & = & u^n + dt\cdot \mathcal{L}(t^n + dt/2, v^{(1)})/2,\\ v^{(3)} & = & u^n + dt\cdot \mathcal{L}(t^n + dt/2, v^{(2)}),\\ v^{(4)} & = & u^n + dt\cdot \mathcal{L}(t^n + dt, v^{(3)}),\\ u^{n+1} & = & (2v^{(1)} + 4v^{(2)} + 2v^{(3)} + v^{(4)} - 3 u^n)/6. \end{eqnarray}

Note that in the implementation, the expression for \(u^{n+1}\) is computed simultaneously with \(v^{(4)}\), so that there are actually only four substeps per step.

The CFL factor/stable step size is 1.3926467817026411.

Member Function Documentation

butcher_tableau()

const ButcherTableau & TimeSteppers::ClassicalRungeKutta4::butcher_tableau ( ) const

overridevirtual

Implements TimeSteppers::RungeKutta.

order()

variants::TaggedVariant< Tags::FixedOrder, Tags::VariableOrder > TimeSteppers::ClassicalRungeKutta4::order ( ) const

overridevirtual

The convergence order of the stepper.

Implements TimeStepper.

stable_step()

double TimeSteppers::ClassicalRungeKutta4::stable_step ( ) const

overridevirtual

Rough estimate of the maximum step size this method can take stably as a multiple of the step for Euler's method.

Implements TimeStepper.

Member Data Documentation

help

Options::String TimeSteppers::ClassicalRungeKutta4::help

staticconstexpr

Initial value:

= {
      "The standard fourth-order Runge-Kutta time-stepper."}

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The documentation for this class was generated from the following file:

• src/Time/TimeSteppers/ClassicalRungeKutta4.hpp