Explicit RK Merson Butcher Tableau. More...

#include <Tempus_RKButcherTableau.hpp>

Inheritance diagram for Tempus::ExplicitMerson45_RKBT< Scalar >:

Public Member Functions
	ExplicitMerson45_RKBT ()

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

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

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

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::ExplicitMerson45_RKBT< Scalar >

Explicit RK Merson Butcher Tableau.

The tableau (order=4(5)) is

$\begin{array}{c|c} c & A \\ \hline & b^T \\ \hline & \hat{b}^T \end{array} \;\;\;\;\mbox{ where }\;\;\;\; \begin{array}{c|ccccc} 0 & 0 & & & & \\ 1/3 & 1/3 & 0 & & & \\ 1/3 & 1/6 & 1/6 & 0 & & \\ 1/2 & 1/8 & 0 & 3/8 & & \\ 1 & 1/2 & 0 & -3/2 & 2 & \\ \hline & 1/6 & 0 & 0 & 2/3 & 1/6 \\ & 1/10 & 0 & 3/10 & 2/5 & 1/5 \end{array}$

Reference: E. Hairer, S.P. Norsett, G. Wanner, "Solving Ordinary Differential Equations I: Nonstiff Problems", 2nd Revised Edition, Table 4.1, pg 167.

Definition at line 836 of file Tempus_RKButcherTableau.hpp.