TNL::Solvers::ODE::Methods::DormandPrince< Value > Struct Template Reference

Fifth order Dormand-Prince method also known as ode45 from Matlab with adaptive step size. More...

#include <TNL/Solvers/ODE/Methods/DormandPrince.h>

Collaboration diagram for TNL::Solvers::ODE::Methods::DormandPrince< Value >:

Public Types
using	ValueType = Value

Static Public Member Functions
static constexpr ValueType	getCoefficient (const std::size_t stage, const std::size_t i)
static constexpr ValueType	getErrorCoefficient (std::size_t i)
static constexpr std::size_t	getStages ()
static constexpr ValueType	getTimeCoefficient (std::size_t i)
static constexpr ValueType	getUpdateCoefficient (std::size_t i)
static constexpr bool	isAdaptive ()

Static Protected Attributes
static constexpr std::array< Value, Stages >	higher_order_update_coefficients { 35.0/384.0, 0.0, 500.0/1113.0, 125.0/192.0, -2187.0/6784.0, 11.0/84.0, 0.0 }
static constexpr std::array< std::array< Value, Stages >, Stages >	k_coefficients
static constexpr std::array< Value, Stages >	lower_order_update_coefficients { 5179.0/57600.0, 0.0, 7571.0/16695.0, 393.0/640.0, -92097.0/339200.0, 187.0/2100.0, 1.0/40.0 }
static constexpr std::size_t	Stages = 7
static constexpr std::array< Value, Stages >	time_coefficients { 0.0, 1.0/5.0, 3.0/10.0, 4.0/5.0, 8.0/9.0, 1.0, 1.0 }

Detailed Description

template<typename Value = double>
struct TNL::Solvers::ODE::Methods::DormandPrince< Value >

Fifth order Dormand-Prince method also known as ode45 from Matlab with adaptive step size.

Template Parameters

Value

is arithmetic type used for computations.

Member Data Documentation

k_coefficients

template<typename Value = double>

std::array< std::array< Value, Stages>, Stages > TNL::Solvers::ODE::Methods::DormandPrince< Value >::k_coefficients

staticconstexprprotected

Initial value:

{
      std::array< Value, Stages >{           0.0,              0.0,            0.0,           0.0,             0.0,       0.0 },
      std::array< Value, Stages >{       1.0/5.0,              0.0,            0.0,           0.0,             0.0,       0.0 },
      std::array< Value, Stages >{       3.0/40.0,        9.0/40.0,            0.0,           0.0,             0.0,       0.0 },
      std::array< Value, Stages >{      44.0/45.0,      -56.0/15.0,       32.0/9.0,           0.0,             0.0,       0.0 },
      std::array< Value, Stages >{ 19372.0/6561.0,   -25360.0/2187.0, 64448.0/6561.0,  -212.0/729.0,             0.0,       0.0 },
      std::array< Value, Stages >{  9017.0/3168.0,       -355.0/33.0, 46732.0/5247.0,    49.0/176.0, -5103.0/18656.0,       0.0 },
      std::array< Value, Stages >{     35.0/384.0,             0.0,   500.0/1113.0,   125.0/192.0,  -2187.0/6784.0, 11.0/84.0 }
   }

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

• src/TNL/Solvers/ODE/Methods/DormandPrince.h