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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 dzero.hpp
\brief \f$ D_{0} \f$ matricial representation
\fullpath
ql/FiniteDifferences/%dzero.hpp
*/
// $Id: dzero.hpp,v 1.8 2002/01/16 14:43:25 nando Exp $
#ifndef quantlib_d_zero_h
#define quantlib_d_zero_h
#include <ql/FiniteDifferences/tridiagonaloperator.hpp>
namespace QuantLib {
namespace FiniteDifferences {
//! \f$ D_{0} \f$ matricial representation
/*! The differential operator \f$ D_{0} \f$ discretizes the
first derivative with the second-order formula
\f[ \frac{\partial u_{i}}{\partial x} \approx
\frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i}
\f]
*/
class DZero : public TridiagonalOperator {
public:
DZero(Size gridPoints, double h);
};
// inline definitions
inline DZero::DZero(Size gridPoints, double h)
: TridiagonalOperator(gridPoints) {
setFirstRow(-1/h,1/h); // linear extrapolation
setMidRows(-1/(2*h),0.0,1/(2*h));
setLastRow(-1/h,1/h); // linear extrapolation
}
}
}
#endif
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