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/*
Copyright (C) 2000, 2001, 2002 RiskMap srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it under the
terms of the QuantLib license. You should have received a copy of the
license along with this program; if not, please email ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file dplusdminus.hpp
\brief \f$ D_{+}D_{-} \f$ matricial representation
\fullpath
ql/FiniteDifferences/%dplusdminus.hpp
*/
// $Id: dplusdminus.hpp,v 1.9 2002/01/16 14:43:25 nando Exp $
#ifndef quantlib_d_plus_d_minus_h
#define quantlib_d_plus_d_minus_h
#include <ql/FiniteDifferences/tridiagonaloperator.hpp>
namespace QuantLib {
namespace FiniteDifferences {
//! \f$ D_{+}D_{-} \f$ matricial representation
/*! The differential operator \f$ D_{+}D_{-} \f$ discretizes the
second derivative with the second-order formula
\f[ \frac{\partial^2 u_{i}}{\partial x^2} \approx
\frac{u_{i+1}-2u_{i}+u_{i-1}}{h^2} = D_{+}D_{-} u_{i}
\f]
*/
class DPlusDMinus : public TridiagonalOperator {
public:
DPlusDMinus(Size gridPoints, double h);
};
// inline definitions
inline DPlusDMinus::DPlusDMinus(Size gridPoints, double h)
: TridiagonalOperator(gridPoints) {
setFirstRow(0.0,0.0); // linear extrapolation
setMidRows(1/(h*h),-2/(h*h),1/(h*h));
setLastRow(0.0,0.0); // linear extrapolation
}
}
}
#endif
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