MathTL::ExplicitRungeKuttaScheme< VECTOR > Class Template Reference

#include <runge_kutta.h>

Inheritance diagram for MathTL::ExplicitRungeKuttaScheme< VECTOR >:

List of all members.

Public Types
enum	Method {   RK12, RK23, Fehlberg34, DoPri45,   DoPri78 }
Public Member Functions
	ExplicitRungeKuttaScheme (const Method method)
void	increment (const AbstractIVP< VECTOR > *ivp, const double t_m, const VECTOR &u_m, const double tau, VECTOR &u_mplus1, VECTOR &error_estimate, const double tolerance=1e-2) const
int	order () const
Protected Attributes
bool	fsal
Vector< double >	c
	node vector
LowerTriangularMatrix< double >	A
	Butcher coefficients.
Vector< double >	b
	weight vectors
Vector< double >	bhat
int	p
	consistency

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Detailed Description

template<class VECTOR>
class MathTL::ExplicitRungeKuttaScheme< VECTOR >

The following class models an s-stage explicit (embedded) Runge-Kutta method for the numerical solution of (abstract) nonautonomous initial value problems of the form

u'(t) = F(t, u(t)), u(0) = u_0.

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Member Enumeration Documentation

template<class VECTOR >

enum MathTL::ExplicitRungeKuttaScheme::Method

enum type for different builtin RK schemes

References: [DB] Deuflhard/Bornemann, Numerische Mathematik II, de Gruyter [S] B.A.Schmitt, Numerik IIb, Vorlesungsskript

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Constructor & Destructor Documentation

template<class VECTOR >

MathTL::ExplicitRungeKuttaScheme< VECTOR >::ExplicitRungeKuttaScheme

(

const Method

method

)

constructor from one of the builtin RK schemes

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Member Function Documentation

template<class VECTOR >

void MathTL::ExplicitRungeKuttaScheme< VECTOR >::increment	(	const AbstractIVP< VECTOR > *	ivp,
		const double	t_m,
		const VECTOR &	u_m,
		const double	tau,
		VECTOR &	u_mplus1,
		VECTOR &	error_estimate,
		const double	tolerance = 1e-2
	)		const [virtual]

increment function + local error estimation

Implements MathTL::OneStepScheme< VECTOR >.

template<class VECTOR >

int MathTL::ExplicitRungeKuttaScheme< VECTOR >::order

(

)

const [inline, virtual]

consistency/convergence order p

Implements MathTL::OneStepScheme< VECTOR >.

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Member Data Documentation

template<class VECTOR >

bool MathTL::ExplicitRungeKuttaScheme< VECTOR >::fsal [protected]

"first same as last" flag (i.e., the first f-evaluation in the next time step is the last one of the current step)

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

• numerics/runge_kutta.h
• numerics/runge_kutta.cpp