Diagonally Implicit Runge-Kutta (DIRK) time stepper. More...

#include <Tempus_StepperDIRK_decl.hpp>

Inheritance diagram for Tempus::StepperDIRK< Scalar >:

Public Member Functions
std::vector< Teuchos::RCP < Thyra::VectorBase< Scalar > > > &	getStageXDot ()

Teuchos::RCP < Thyra::VectorBase< Scalar > > &	getXTilde ()

virtual Scalar	getAlpha (const Scalar dt) const
	Return alpha = d(xDot)/dx. More...

virtual Scalar	getBeta (const Scalar) const
	Return beta = d(x)/dx. More...

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

virtual bool	isValidSetup (Teuchos::FancyOStream &out) const

Basic stepper methods
virtual void	setObserver (Teuchos::RCP< StepperObserver< Scalar > > obs=Teuchos::null)
	Set Observer. More...

virtual Teuchos::RCP < StepperObserver< Scalar > >	getObserver () const
	Get Observer. More...

virtual void	initialize ()
	Initialize after construction and changing input parameters. More...

virtual void	setInitialConditions (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Set the initial conditions and make them consistent. More...

virtual void	setResetInitialGuess (bool reset_guess)
	Set parameter so that the initial guess is reset at the beginning of each timestep. More...

virtual bool	getResetInitialGuess () const

virtual void	takeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &solutionHistory)
	Take the specified timestep, dt, and return true if successful. More...

virtual Teuchos::RCP < Tempus::StepperState< Scalar > >	getDefaultStepperState ()
	Get a default (initial) StepperState. More...

virtual bool	isExplicit () const

virtual bool	isImplicit () const

virtual bool	isExplicitImplicit () const

virtual bool	isOneStepMethod () const

virtual bool	isMultiStepMethod () const

virtual OrderODE	getOrderODE () const

void	getValidParametersBasicDIRK (Teuchos::RCP< Teuchos::ParameterList > pl) const

virtual std::string	getDescription () const =0

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

Accessors methods
virtual void	setUseEmbedded (bool a)
	Use embedded if avialable. More...

virtual bool	getUseEmbedded () const

virtual bool	getUseEmbeddedDefault () const

Public Member Functions inherited from Tempus::StepperImplicit< Scalar >
virtual void	setModel (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &appModel)

virtual Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > >	getModel ()

virtual Teuchos::RCP< const WrapperModelEvaluator< Scalar > >	getWrapperModel ()

virtual void	setDefaultSolver ()

virtual void	setSolver (Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > solver)
	Set solver. More...

virtual Teuchos::RCP < Thyra::NonlinearSolverBase < Scalar > >	getSolver () const
	Get solver. More...

const Thyra::SolveStatus< Scalar >	solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x)
	Solve problem using x in-place. (Needs to be deprecated!) More...

const Thyra::SolveStatus< Scalar >	solveImplicitODE (const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Solve implicit ODE, f(x, xDot, t, p) = 0. More...

void	evaluateImplicitODE (Teuchos::RCP< Thyra::VectorBase< Scalar > > &f, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &x, const Teuchos::RCP< Thyra::VectorBase< Scalar > > &xDot, const Scalar time, const Teuchos::RCP< ImplicitODEParameters< Scalar > > &p)
	Evaluate implicit ODE residual, f(x, xDot, t, p). More...

virtual void	setInitialGuess (Teuchos::RCP< const Thyra::VectorBase< Scalar > > initialGuess)
	Pass initial guess to Newton solver (only relevant for implicit solvers) More...

virtual void	setZeroInitialGuess (bool zIG)
	Set parameter so that the initial guess is set to zero (=True) or use last timestep (=False). More...

virtual bool	getZeroInitialGuess () const

virtual Scalar	getInitTimeStep (const Teuchos::RCP< SolutionHistory< Scalar > > &) const

Public Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	setNonConstModel (const Teuchos::RCP< Thyra::ModelEvaluator< Scalar > > &)

virtual bool	isInitialized ()
	True if stepper's member data is initialized. More...

virtual void	checkInitialized ()
	Check initialization, and error out on failure. More...

void	setStepperType (std::string s)

std::string	getStepperType () const

void	setUseFSAL (bool a)

bool	getUseFSAL () const

virtual bool	getUseFSALDefault () const

void	setICConsistency (std::string s)

std::string	getICConsistency () const

virtual std::string	getICConsistencyDefault () const

void	setICConsistencyCheck (bool c)

bool	getICConsistencyCheck () const

virtual bool	getICConsistencyCheckDefault () const

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperX (Teuchos::RCP< SolutionState< Scalar > > state)
	Get x from SolutionState or Stepper storage. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDot (Teuchos::RCP< SolutionState< Scalar > > state)
	Get xDot from SolutionState or Stepper storage. More...

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStepperXDotDot (Teuchos::RCP< SolutionState< Scalar > > state)
	Get xDotDot from SolutionState or Stepper storage. More...

virtual std::string	description () const

virtual void	createSubSteppers (std::vector< Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > >)

Public Member Functions inherited from Tempus::StepperRKBase< Scalar >
virtual Teuchos::RCP< const RKButcherTableau< Scalar > >	getTableau () const

virtual Scalar	getOrder () const

virtual Scalar	getOrderMin () const

virtual Scalar	getOrderMax () const

virtual int	getNumberOfStages () const

virtual int	getStageNumber () const

virtual void	setStageNumber (int s)

virtual Teuchos::RCP < Thyra::VectorBase< Scalar > >	getStageX ()

virtual Teuchos::RCP< const Thyra::VectorBase< Scalar > >	getStageX () const

virtual void	setAppAction (Teuchos::RCP< StepperRKAppAction< Scalar > > appAction)

virtual Teuchos::RCP < StepperRKAppAction< Scalar > >	getAppAction () const

Protected Member Functions
virtual void	setupDefault ()
	Default setup for constructor. More...

virtual void	setup (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &wrapperModel, const Teuchos::RCP< StepperRKObserver< Scalar > > &obs, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool useEmbedded, bool zeroInitialGuess)
	Setup for constructor. More...

virtual void	setup (const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &wrapperModel, const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &solver, bool useFSAL, std::string ICConsistency, bool ICConsistencyCheck, bool useEmbedded, bool zeroInitialGuess, const Teuchos::RCP< StepperRKAppAction< Scalar > > &stepperRKAppAction)

virtual void	setupTableau ()=0

Protected Member Functions inherited from Tempus::Stepper< Scalar >
virtual void	setStepperX (Teuchos::RCP< Thyra::VectorBase< Scalar > > x)
	Set x for Stepper storage. More...

virtual void	setStepperXDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDot)
	Set xDot for Stepper storage. More...

virtual void	setStepperXDotDot (Teuchos::RCP< Thyra::VectorBase< Scalar > > xDotDot)
	Set x for Stepper storage. More...

Protected Attributes
std::vector< Teuchos::RCP < Thyra::VectorBase< Scalar > > >	stageXDot_

Teuchos::RCP < Thyra::VectorBase< Scalar > >	xTilde_

Teuchos::RCP < StepperRKObserverComposite < Scalar > >	stepperObserver_

bool	useEmbedded_

Teuchos::RCP < Thyra::VectorBase< Scalar > >	ee_

Teuchos::RCP < Thyra::VectorBase< Scalar > >	abs_u0

Teuchos::RCP < Thyra::VectorBase< Scalar > >	abs_u

Teuchos::RCP < Thyra::VectorBase< Scalar > >	sc

bool	resetGuess_ = true

Protected Attributes inherited from Tempus::StepperImplicit< Scalar >
Teuchos::RCP < WrapperModelEvaluator < Scalar > >	wrapperModel_

Teuchos::RCP < Thyra::NonlinearSolverBase < Scalar > >	solver_

Teuchos::RCP< const Thyra::VectorBase< Scalar > >	initialGuess_

bool	zeroInitialGuess_

Teuchos::RCP< StepperObserver < Scalar > >	stepperObserver_

Protected Attributes inherited from Tempus::Stepper< Scalar >
bool	isInitialized_ = false
	True if stepper's member data is initialized. More...

Protected Attributes inherited from Tempus::StepperRKBase< Scalar >
Teuchos::RCP< RKButcherTableau < Scalar > >	tableau_

int	stageNumber_
	The current Runge-Kutta stage number, {0,...,s-1}. -1 indicates outside stage loop. More...

Teuchos::RCP < Thyra::VectorBase< Scalar > >	stageX_

Teuchos::RCP < StepperRKAppAction< Scalar > >	stepperRKAppAction_

Detailed Description

template<class Scalar>
class Tempus::StepperDIRK< Scalar >

Diagonally Implicit Runge-Kutta (DIRK) time stepper.

For the implicit ODE system, $\mathcal{F}(\dot{x},x,t) = 0$ , the general DIRK method for $s$ -stages, can be written as

$X_{i} = x_{n-1} + \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\bar{f}(X_{j},t_{n-1}+c_{j}\Delta t) + \Delta t\, a_{ii}\,\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$

$x_{n} = x_{n-1} + \Delta t\,\sum_{i=1}^{s}b_{i}\,\bar{f}(X_{i},t_{n-1}+c_{i}\Delta t)$

where $\dot{x}=\bar{f}(x,t)$ is the explicit form of the ODE, $X_{i}$ are intermediate approximations to the solution at times, $t_{n-1}+c_{i}\Delta t$ , (stage solutions) which may be correct to a lower order of accuracy than the solution, $x_{n}$ . We should note that these lower-order approximations are combined through $b_{i}$ so that error terms cancel out and produce a more accurate solution. Note for DIRK methods that $a_{ii}=a$ for all the diagonal components is referred to as Singly Diagonal Implicit Runge-Kutta (SDIRK) methods.

Note that the stage time derivatives,

$\dot{X}_{i} = \bar{f}(X_{i},t_{n-1}+c_{i}\Delta t),$

can be found via

$\begin{eqnarray*} \dot{X}_{i} & = & \frac{1}{a_{ii} \Delta t} [ X_{i} - x_{n-1} - \Delta t\,\sum_{j=1}^{i-1} a_{ij}\,\dot{X}_{j} ] \\ \dot{X}_{i} & = & \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t} \end{eqnarray*}$

where

$\tilde{X} = x_{n-1} + \Delta t \sum_{j=1}^{i-1} a_{ij}\, \dot{X}_{j}$

Recalling that the definition for a DIRK is that for $j>i$ , $a_{ij} = 0$ and $a_{ii} \neq 0$ for at least one $i$ . Thus for stages where $a_{ii} = 0$ , we can use the explicit RK methods (see StepperExplicitRK for additional details).

Algorithm The single-timestep algorithm for DIRK is

$\begin{algorithm} \renewcommand{\thealgorithm}{} \caption{DIRK with the application-action locations indicated.} \begin{algorithmic}[1] \State {\it appAction.execute(solutionHistory, stepper, BEGIN\_STEP)} \If {``Reset initial guess.''} \State $X \leftarrow x_{n-1}$ \Comment{Reset initial guess to last timestep.} \EndIf \For {$i = 0 \ldots s-1$} \If { $a_{k,i} = 0 \;\forall k = (i+1,\ldots, s-1)$, $b(i) = 0$, $b^\ast(i) = 0$} \State $\dot{X}_i \leftarrow 0$ \Comment{Not needed for later calculations.} \State {\bf continue} \EndIf \State $\tilde{X} \leftarrow x_{n-1} +\Delta t \sum_{j=1}^{i-1} a_{ij}\,\dot{X}_{j}$ \State {\it appAction.execute(solutionHistory, stepper, BEGIN\_STAGE)} \If {$a_{ii} = 0$} \Comment{Explicit stage.} \If {$i=0$ and ``Use FSAL''} \Comment{Save an evaluation?} \State $\dot{X}_0 \leftarrow \dot{X}_{s-1}$ \Comment{Use $\dot{X}_{s-1}$ from $n-1$ time step.} \Else \State $\dot{X}_i \leftarrow \bar{f}(\tilde{X},t_{n-1}+c_i\Delta t)$ \EndIf \Else \Comment{Implicit stage.} \State {\it appAction.execute(solutionHistory, stepper, BEFORE\_SOLVE)} \If {``Zero initial guess.''} \State $X \leftarrow 0$ \Comment{Else use previous stage value as initial guess.} \EndIf \State Solve $\mathcal{F}_i( \dot{X}_i = \frac{X - \tilde{X}}{a_{ii} \Delta t}, X, t_{n-1}+c_{i}\Delta t) = 0$ for $X$ \State {\it appAction.execute(solutionHistory, stepper, AFTER\_SOLVE)} \State $\dot{X}_i \leftarrow \frac{X - \tilde{X}}{a_{ii} \Delta t}$ \EndIf \State {\it appAction.execute(solutionHistory, stepper, BEFORE\_EXPLICIT\_EVAL)} \State {\it appAction.execute(solutionHistory, stepper, END\_STAGE)} \EndFor \State $x_n \leftarrow x_{n-1} + \Delta t\,\sum_{i=0}^{s-1}b_i\,\dot{X}_i$ \If {``Embedded''} \Comment{Compute the local truncation error estimate.} \State $\mathbf{e} \leftarrow \sum_{i=0}^{s-1} (b_i-b^\ast_i)\Delta t\,\dot{X}_i$ \State $\tilde{\mathbf{e}} \leftarrow \mathbf{e}/(a_{tol} + \max(\|x_n\|, \|x_{n-1}\|)r_{tol})$ \State $e_n \leftarrow \|\tilde{\mathbf{e}}\|_\infty$ \EndIf \State {\it appAction.execute(solutionHistory, stepper, END\_STEP)} \end{algorithmic} \end{algorithm}$

The First-Step-As-Last (FSAL) principle is not needed with DIRK, but maybe useful if the first stage is explicit (EDIRK) (e.g., Trapezoidal Method). The default is to set useFSAL=false.

Iteration Matrix, . Recalling that the definition of the iteration matrix, $W$ , is

$W = \alpha \frac{\partial \mathcal{F}_n}{\partial \dot{x}_n} + \beta \frac{\partial \mathcal{F}_n}{\partial x_n},$

where $\alpha \equiv \frac{\partial \dot{x}_n(x_n) }{\partial x_n},$ and $\beta \equiv \frac{\partial x_n}{\partial x_n} = 1$ . For the stage solutions, we have

$\mathcal{F}_i = \dot{X}_{i} - \bar{f}(X_{i},t_{n-1}+c_{i}\Delta t) =0.$

where $\mathcal{F}_n \rightarrow \mathcal{F}_i$ , $x_n \rightarrow X_{i}$ , and $\dot{x}_n(x_n) \rightarrow \dot{X}_{i}(X_{i})$ . The time derivative for the DIRK stages is

$\dot{X}_{i}(X_{i}) = \frac{X_{i} - \tilde{X}}{a_{ii} \Delta t},$

and we can determine that $\alpha = \frac{1}{a_{ii} \Delta t}$ and $\beta = 1$ , and therefore write

$W = \frac{1}{a_{ii} \Delta t} \frac{\partial \mathcal{F}_i}{\partial \dot{X}_i} + \frac{\partial \mathcal{F}_i}{\partial X_i}.$

Definition at line 153 of file Tempus_StepperDIRK_decl.hpp.

Member Function Documentation

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::describe	(	Teuchos::FancyOStream &	out,
		const Teuchos::EVerbosityLevel	verbLevel
	)		const

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 416 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getAlpha ( const Scalar dt ) const

inlinevirtual

Return alpha = d(xDot)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 213 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual Scalar Tempus::StepperDIRK< Scalar >::getBeta ( const Scalar ) const

inlinevirtual

Return beta = d(x)/dx.

Implements Tempus::StepperImplicit< Scalar >.

Definition at line 219 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP< Tempus::StepperState< Scalar > > Tempus::StepperDIRK< Scalar >::getDefaultStepperState ( )

virtual

Get a default (initial) StepperState.

Provide a StepperState to the SolutionState. This Stepper does not have any special state data, so just provide the base class StepperState with the Stepper description. This can be checked to ensure that the input StepperState can be used by this Stepper.

Implements Tempus::Stepper< Scalar >.

Definition at line 407 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual std::string Tempus::StepperDIRK< Scalar >::getDescription ( ) const

pure virtual

template<class Scalar >

virtual Teuchos::RCP<StepperObserver<Scalar> > Tempus::StepperDIRK< Scalar >::getObserver ( ) const

inlinevirtual

Get Observer.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 164 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual OrderODE Tempus::StepperDIRK< Scalar >::getOrderODE ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 201 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::getResetInitialGuess ( ) const

inlinevirtual

Definition at line 177 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > >& Tempus::StepperDIRK< Scalar >::getStageXDot ( )

inline

Definition at line 209 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::getUseEmbedded ( ) const

inlinevirtual

Definition at line 235 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::getUseEmbeddedDefault ( ) const

inlinevirtual

Definition at line 236 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

Teuchos::RCP< const Teuchos::ParameterList > Tempus::StepperDIRK< Scalar >::getValidParameters ( ) const

virtual

Implements Tempus::Stepper< Scalar >.

Definition at line 477 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::getValidParametersBasicDIRK ( Teuchos::RCP< Teuchos::ParameterList > pl ) const

Definition at line 109 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

Teuchos::RCP<Thyra::VectorBase<Scalar> >& Tempus::StepperDIRK< Scalar >::getXTilde ( )

inline

Definition at line 210 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::initialize ( )

virtual

Initialize after construction and changing input parameters.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 160 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::isExplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 187 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::isExplicitImplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 196 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::isImplicit ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 195 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::isMultiStepMethod ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 199 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

virtual bool Tempus::StepperDIRK< Scalar >::isOneStepMethod ( ) const

inlinevirtual

Implements Tempus::Stepper< Scalar >.

Definition at line 198 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

bool Tempus::StepperDIRK< Scalar >::isValidSetup ( Teuchos::FancyOStream & out ) const

virtual

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 448 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::setInitialConditions ( const Teuchos::RCP< SolutionHistory< Scalar > > & solutionHistory )

virtual

Set the initial conditions and make them consistent.

Reimplemented from Tempus::StepperImplicit< Scalar >.

Definition at line 185 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::setObserver ( Teuchos::RCP< StepperObserver< Scalar > > obs = Teuchos::null )

virtual

Set Observer.

Reimplemented from Tempus::Stepper< Scalar >.

Definition at line 129 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

virtual void Tempus::StepperDIRK< Scalar >::setResetInitialGuess ( bool reset_guess )

inlinevirtual

Set parameter so that the initial guess is reset at the beginning of each timestep.

Definition at line 175 of file Tempus_StepperDIRK_decl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::setup	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	wrapperModel,
		const Teuchos::RCP< StepperRKObserver< Scalar > > &	obs,
		const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &	solver,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	useEmbedded,
		bool	zeroInitialGuess
	)

protectedvirtual

Setup for constructor.

Definition at line 46 of file Tempus_StepperDIRK_impl.hpp.

template<class Scalar >

void Tempus::StepperDIRK< Scalar >::setup	(	const Teuchos::RCP< const Thyra::ModelEvaluator< Scalar > > &	wrapperModel,
		const Teuchos::RCP< Thyra::NonlinearSolverBase< Scalar > > &	solver,
		bool	useFSAL,
		std::string	ICConsistency,
		bool	ICConsistencyCheck,
		bool	useEmbedded,
		bool	zeroInitialGuess,
		const Teuchos::RCP< StepperRKAppAction< Scalar > > &	stepperRKAppAction
	)