timestepping::RungeKutta2 Class Reference

Timestep strategy for the explicit 2nd order RungeKutta algorithm to solve first order problems in time. More...

#include <rungekutta2.hh>

Inheritance diagram for timestepping::RungeKutta2:

Public Member Functions
	RungeKutta2 (concepts::SolverFabric< Real > &fabric, concepts::Operator< Real > &D1, concepts::Operator< Real > &D0, timestepping::TimeVector &trhs, const concepts::Vector< Real > &Y0, Real dt, Real alpha=0.5)
	Constructor. More...
virtual	~RungeKutta2 ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...
virtual void	next ()
	The overloaded member function next() has to calculate the new right hand side and to release the solution vector. More...

Protected Attributes
Real	dt_
	Time step size. More...
concepts::Operator< Real > *	liCo_
	Operator of the linear equation system which is solved by the friend class TimeStepping. More...
concepts::Vector< Real >	rhs_
	The right hand side vector of the linear equation system which is solved by the friend class TimeStepping. More...
concepts::Vector< Real >	sol_
	The solution vector of the linear equation system which is solved by the friend class TimeStepping. More...
std::unique_ptr< concepts::Operator< Real > >	solver_
	Solver for the linear system. More...
Real	t_
	Time of the actual solution. More...

Private Attributes
Real	alpha_
	Parameters of the scheme. More...
concepts::Operator< Real > &	D0_
	Space operator. More...
timestepping::TimeVector &	trhs_
	External driver function. More...
concepts::Vector< Real >	Yn1_
	Store the latest timestep. More...

Detailed Description

Timestep strategy for the explicit 2nd order RungeKutta algorithm to solve first order problems in time.

The scheme has one free parameter alpha and has convergence order 2. Please notice that this algorithm is not absolutely stable and may not converge if the stability condition is not fullfilled.

See also

H. R. Schwarz Numerische Mathematik, Teubner, 1997

Author

Manuel Walser, 2002

Definition at line 37 of file rungekutta2.hh.

Constructor & Destructor Documentation

RungeKutta2()

timestepping::RungeKutta2::RungeKutta2	(	concepts::SolverFabric< Real > &	fabric,
		concepts::Operator< Real > &	D1,
		concepts::Operator< Real > &	D0,
		timestepping::TimeVector &	trhs,
		const concepts::Vector< Real > &	Y0,
		Real	dt,
		Real	alpha = 0.5
	)

Constructor.

Parameters

fabric	Solver fabric for solving the occuring systems
D1	Space opeartor D1
D0	Space opeartor D0
trhs	Timedependent external driver f(x,t)
Y0	Initial condition y(x,0)
dt	Time step size
alpha	Parameter of the Runge Kutta 2 scheme

~RungeKutta2()

virtual timestepping::RungeKutta2::~RungeKutta2 ( )

virtual

Member Function Documentation

info()

virtual std::ostream& timestepping::RungeKutta2::info ( std::ostream &  os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

next()

virtual void timestepping::RungeKutta2::next ( )

protectedvirtual

The overloaded member function next() has to calculate the new right hand side and to release the solution vector.

Then the Timestepping solver can set the new solution.

Implements timestepping::TimeStepStrategy.

Member Data Documentation

alpha_

Real timestepping::RungeKutta2::alpha_

private

Parameters of the scheme.

Definition at line 67 of file rungekutta2.hh.

D0_

concepts::Operator<Real>& timestepping::RungeKutta2::D0_

private

Space operator.

Definition at line 61 of file rungekutta2.hh.

dt_

Real timestepping::TimeStepStrategy::dt_

protectedinherited

Time step size.

Definition at line 77 of file strategy.hh.

liCo_

concepts::Operator<Real>* timestepping::TimeStepStrategy::liCo_

protectedinherited

Operator of the linear equation system which is solved by the friend class TimeStepping.

It can be stored as a linear combination of two operators. The exact form depends on the specific scheme.

See also

TimeStepping

Definition at line 65 of file strategy.hh.

rhs_

concepts::Vector<Real> timestepping::TimeStepStrategy::rhs_

protectedinherited

The right hand side vector of the linear equation system which is solved by the friend class TimeStepping.

See also

TimeStepping

Definition at line 75 of file strategy.hh.

sol_

concepts::Vector<Real> timestepping::TimeStepStrategy::sol_

protectedinherited

The solution vector of the linear equation system which is solved by the friend class TimeStepping.

See also

TimeStepping

Definition at line 70 of file strategy.hh.

solver_

std::unique_ptr<concepts::Operator<Real> > timestepping::TimeStepStrategy::solver_

protectedinherited

Solver for the linear system.

Definition at line 59 of file strategy.hh.

t_

Real timestepping::TimeStepStrategy::t_

protectedinherited

Time of the actual solution.

Definition at line 79 of file strategy.hh.

trhs_

timestepping::TimeVector& timestepping::RungeKutta2::trhs_

private

External driver function.

Definition at line 63 of file rungekutta2.hh.

Yn1_

concepts::Vector<Real> timestepping::RungeKutta2::Yn1_

private

Store the latest timestep.

Definition at line 65 of file rungekutta2.hh.

---

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

• timestepping/rungekutta2.hh