SDIRK 2 Stage 3rd order. More...

#include <Tempus_RKButcherTableau.hpp>

Inheritance diagram for Tempus::SDIRK2Stage3rdOrder_RKBT< Scalar >:

Public Member Functions
	SDIRK2Stage3rdOrder_RKBT ()

void	setParameterList (Teuchos::RCP< Teuchos::ParameterList > const &pList)

Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const

virtual std::string	description () const

Public Member Functions inherited from Tempus::RKButcherTableau< Scalar >
virtual std::size_t	numStages () const
	Return the number of stages. More...

virtual const Teuchos::SerialDenseMatrix< int, Scalar > &	A () const
	Return the matrix coefficients. More...

virtual const Teuchos::SerialDenseVector< int, Scalar > &	b () const
	Return the vector of quadrature weights. More...

virtual const Teuchos::SerialDenseVector< int, Scalar > &	bstar () const
	Return the vector of quadrature weights for embedded methods. More...

virtual const Teuchos::SerialDenseVector< int, Scalar > &	c () const
	Return the vector of stage positions. More...

virtual int	order () const
	Return the order. More...

virtual int	orderMin () const
	Return the minimum order. More...

virtual int	orderMax () const
	Return the maximum order. More...

virtual bool	isImplicit () const
	Return true if the RK method is implicit. More...

virtual bool	isDIRK () const
	Return true if the RK method is Diagonally Implicit. More...

virtual bool	isEmbedded () const
	Return true if the RK method has embedded capabilities. More...

virtual void	initialize (const Teuchos::SerialDenseMatrix< int, Scalar > &A, const Teuchos::SerialDenseVector< int, Scalar > &b, const Teuchos::SerialDenseVector< int, Scalar > &c, const int order, const std::string &longDescription, bool isEmbedded=false, const Teuchos::SerialDenseVector< int, Scalar > &bstar=Teuchos::SerialDenseVector< int, Scalar >())

virtual void	initialize (const Teuchos::SerialDenseMatrix< int, Scalar > &A, const Teuchos::SerialDenseVector< int, Scalar > &b, const Teuchos::SerialDenseVector< int, Scalar > &c, const int order, const int orderMin, const int orderMax, const std::string &longDescription, bool isEmbedded=false, const Teuchos::SerialDenseVector< int, Scalar > &bstar=Teuchos::SerialDenseVector< int, Scalar >())

virtual void	describe (Teuchos::FancyOStream &out, const Teuchos::EVerbosityLevel verbLevel) const

Private Attributes
bool	thirdOrderAStable_default_

bool	thirdOrderAStable_

bool	secondOrderLStable_default_

bool	secondOrderLStable_

Scalar	gamma_default_

Scalar	gamma_

Additional Inherited Members
Protected Member Functions inherited from Tempus::RKButcherTableau< Scalar >
virtual void	setDescription (std::string longD)

const std::string &	getDescription () const

void	set_A (const Teuchos::SerialDenseMatrix< int, Scalar > &A)

void	set_b (const Teuchos::SerialDenseVector< int, Scalar > &b)

void	set_c (const Teuchos::SerialDenseVector< int, Scalar > &c)

void	set_order (const int &order)

void	set_orderMin (const int &order)

void	set_orderMax (const int &order)

void	set_isImplicit ()

void	set_isDIRK ()
	DIRK is defined as if a_ij = 0 for j>i and a_ii != 0 for at least one i. More...

Protected Attributes inherited from Tempus::RKButcherTableau< Scalar >
Teuchos::RCP< Teuchos::ParameterList >	rkbtPL_

Detailed Description

template<class Scalar>
class Tempus::SDIRK2Stage3rdOrder_RKBT< Scalar >

SDIRK 2 Stage 3rd order.

The tableau (order=2 or 3) is

$\begin{array}{c|c} c & A \\ \hline & b^T \end{array} \;\;\;\;\mbox{ where }\;\;\;\; \begin{array}{c|cc} \gamma & \gamma & \\ 1-\gamma & 1-2\gamma & \gamma \\ \hline & 1/2 & 1/2 \end{array}$

$\gamma = \left\{ \begin{array}{cc} (2\pm \sqrt{2})/2 & \mbox{then 2nd order and L-stable} \\ (3\pm \sqrt{3})/6 & \mbox{then 3rd order and A-stable} \end{array} \right.$

The default value is $\gamma = (3\pm \sqrt{3})/6$ .

Reference: E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd Revised Edition, Table 7.2, pg 207.

Definition at line 1892 of file Tempus_RKButcherTableau.hpp.