MathTL::OneStepScheme< VECTOR > Class Template Reference

#include <one_step_scheme.h>

Inheritance diagram for MathTL::OneStepScheme< VECTOR >:

List of all members.

Public Member Functions
virtual	~OneStepScheme ()=0
virtual 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 =0
virtual int	order () const =0

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Detailed Description

template<class VECTOR>
class MathTL::OneStepScheme< VECTOR >

Abstract base class for various one-step schemes for the adaptive numerical solution of vector-valued initial value problems

u'(t) = f(t, u(t)), 0 < t <= T u(0) = u_0

where u:[0,T]->V. A one-step schemes essentially has to perform the increment u^{(m)}->u^{(m+1)}, where u^{(m)} is an approximation of u(t_m) for a given time sequence 0=t_0<t_1<... Additionally, the increment function has to provide some local error estimator.

Since the one-step scheme may also be used in an infinite-dimensional setting, it is possible to specify a tolerance parameter (which controls the overall spatial error introduced by the evaluations of the right-hand side).

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Constructor & Destructor Documentation

template<class VECTOR >

MathTL::OneStepScheme< VECTOR >::~OneStepScheme

(

)

[pure virtual]

virtual destructor

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Member Function Documentation

template<class VECTOR>

virtual void MathTL::OneStepScheme< 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 [pure virtual]

increment function u^{(m)} -> u^{(m+1)}, also returns a local error estimator

Implemented in MathTL::WMethod< VECTOR >, and MathTL::ExplicitRungeKuttaScheme< VECTOR >.

template<class VECTOR>

virtual int MathTL::OneStepScheme< VECTOR >::order

(

)

const [pure virtual]

consistency/convergence order of the scheme

Implemented in MathTL::WMethod< VECTOR >, and MathTL::ExplicitRungeKuttaScheme< VECTOR >.

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

• numerics/one_step_scheme.h
• numerics/one_step_scheme.cpp