\( D_{0} \) matricial representation More...

#include <ql/methods/finitedifferences/dzero.hpp>

Inheritance diagram for DZero:

Public Member Functions
	DZero (Size gridPoints, Real h)

Public Member Functions inherited from TridiagonalOperator
	TridiagonalOperator (Size size=0)

	TridiagonalOperator (const Array &low, const Array &mid, const Array &high)

	TridiagonalOperator (const Disposable< TridiagonalOperator > &)

TridiagonalOperator &	operator= (const Disposable< TridiagonalOperator > &)

Size	size () const

bool	isTimeDependent () const

const Array &	lowerDiagonal () const

const Array &	diagonal () const

const Array &	upperDiagonal () const

void	setFirstRow (Real, Real)

void	setMidRow (Size, Real, Real, Real)

void	setMidRows (Real, Real, Real)

void	setLastRow (Real, Real)

void	setTime (Time t)

void	swap (TridiagonalOperator &)

Disposable< Array >	applyTo (const Array &v) const
	apply operator to a given array

Disposable< Array >	solveFor (const Array &rhs) const
	solve linear system for a given right-hand side

void	solveFor (const Array &rhs, Array &result) const

Disposable< Array >	SOR (const Array &rhs, Real tol) const
	solve linear system with SOR approach

Additional Inherited Members
Public Types inherited from TridiagonalOperator
typedef Array	array_type

Static Public Member Functions inherited from TridiagonalOperator
static Disposable< TridiagonalOperator >	identity (Size size)
	identity instance

Protected Attributes inherited from TridiagonalOperator
Size	n_

Array	diagonal_

Array	lowerDiagonal_

Array	upperDiagonal_

Array	temp_

ext::shared_ptr< TimeSetter >	timeSetter_

Detailed Description

\( D_{0} \) matricial representation

The differential operator \( D_{0} \) discretizes the first derivative with the second-order formula

\[ \frac{\partial u_{i}}{\partial x} \approx \frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i} \]

Tests:: the correctness of the returned values is tested by checking them against numerical calculations.

Public Member Functions