TimeSteppers::DormandPrince5 Class Reference

#include <DormandPrince5.hpp>

Public Types
using	options = tmpl::list<>

Public Member Functions
	DormandPrince5 (const DormandPrince5 &) noexcept=default
DormandPrince5 &	operator= (const DormandPrince5 &) noexcept=default
	DormandPrince5 (DormandPrince5 &&) noexcept=default
DormandPrince5 &	operator= (DormandPrince5 &&) noexcept=default
template<typename Vars , typename DerivVars >
void	update_u (gsl::not_null< Vars * > u, gsl::not_null< History< Vars, DerivVars > * > history, const TimeDelta &time_step) const noexcept
template<typename Vars , typename ErrVars , typename DerivVars >
bool	update_u (gsl::not_null< Vars * > u, gsl::not_null< ErrVars * > u_error, gsl::not_null< History< Vars, DerivVars > * > history, const TimeDelta &time_step) const noexcept
template<typename Vars , typename DerivVars >
bool	dense_update_u (gsl::not_null< Vars * > u, const History< Vars, DerivVars > &history, double time) const noexcept
size_t	order () const noexcept override
size_t	error_estimate_order () const noexcept override
uint64_t	number_of_substeps () const noexcept override
uint64_t	number_of_substeps_for_error () const noexcept override
size_t	number_of_past_steps () const noexcept override
double	stable_step () const noexcept override
TimeStepId	next_time_id (const TimeStepId &current_id, const TimeDelta &time_step) const noexcept override
TimeStepId	next_time_id_for_error (const TimeStepId &current_id, const TimeDelta &time_step) const noexcept override
template<typename Vars , typename DerivVars >
bool	can_change_step_size (const TimeStepId &time_id, const TimeSteppers::History< Vars, DerivVars > &) const noexcept
	WRAPPED_PUPable_decl_template (DormandPrince5)
	DormandPrince5 (CkMigrateMessage *) noexcept
void	pup (PUP::er &p) noexcept override
template<typename Vars , typename DerivVars >
void	update_u (const gsl::not_null< Vars * > u, const gsl::not_null< History< Vars, DerivVars > * > history, const TimeDelta &time_step) const noexcept
template<typename Vars , typename ErrVars , typename DerivVars >
bool	update_u (const gsl::not_null< Vars * > u, const gsl::not_null< ErrVars * > u_error, const gsl::not_null< History< Vars, DerivVars > * > history, const TimeDelta &time_step) const noexcept
template<typename Vars , typename DerivVars >
bool	dense_update_u (const gsl::not_null< Vars * > u, const History< Vars, DerivVars > &history, const double time) const noexcept

Static Public Attributes
static constexpr Options::String	help

Detailed Description

The standard 5th-order Dormand-Prince time stepping method, given e.g. in Sec. 7.2 of [90].

\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{align} k^{(1)} & = dt \mathcal{L}(t^n, u^n),\\ k^{(i)} & = dt \mathcal{L}(t^n + c_i dt, u^n + \sum_{j=1}^{i-1} a_{ij} k^{(j)}), \mbox{ } 2 \leq i \leq 6,\\ u^{n+1} & = u^n + \sum_{i=1}^{6} b_i k^{(i)}. \end{align}

Here the coefficients \(a_{ij}\), \(b_i\), and \(c_i\) are given in e.g. Sec. 7.2 of [90]. Note that \(c_1 = 0\).

Member Data Documentation

help

constexpr Options::String TimeSteppers::DormandPrince5::help

staticconstexpr

Initial value:

= {
      "The standard Dormand-Prince 5th-order time stepper."}