1 /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ 2 3 /* 4 Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl 5 6 This file is part of QuantLib, a free-software/open-source library 7 for financial quantitative analysts and developers - http://quantlib.org/ 8 9 QuantLib is free software: you can redistribute it and/or modify it 10 under the terms of the QuantLib license. You should have received a 11 copy of the license along with this program; if not, please email 12 <quantlib-dev@lists.sf.net>. The license is also available online at 13 <http://quantlib.org/license.shtml>. 14 15 This program is distributed in the hope that it will be useful, but WITHOUT 16 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS 17 FOR A PARTICULAR PURPOSE. See the license for more details. 18 */ 19 20 /*! \file dplusdminus.hpp 21 \brief \f$ D_{+}D_{-} \f$ matricial representation 22 */ 23 24 #ifndef quantlib_d_plus_d_minus_h 25 #define quantlib_d_plus_d_minus_h 26 27 #include <ql/methods/finitedifferences/tridiagonaloperator.hpp> 28 29 namespace QuantLib { 30 31 //! \f$ D_{+}D_{-} \f$ matricial representation 32 /*! The differential operator \f$ D_{+}D_{-} \f$ discretizes the 33 second derivative with the second-order formula 34 \f[ \frac{\partial^2 u_{i}}{\partial x^2} \approx 35 \frac{u_{i+1}-2u_{i}+u_{i-1}}{h^2} = D_{+}D_{-} u_{i} 36 \f] 37 38 \ingroup findiff 39 40 \test the correctness of the returned values is tested by 41 checking them against numerical calculations. 42 */ 43 class DPlusDMinus : public TridiagonalOperator { 44 public: 45 DPlusDMinus(Size gridPoints, Real h); 46 }; 47 48 49 // inline definitions 50 DPlusDMinus(Size gridPoints,Real h)51 inline DPlusDMinus::DPlusDMinus(Size gridPoints, Real h) 52 : TridiagonalOperator(gridPoints) { 53 setFirstRow(0.0,0.0); // linear extrapolation 54 setMidRows(1/(h*h),-2/(h*h),1/(h*h)); 55 setLastRow(0.0,0.0); // linear extrapolation 56 } 57 58 } 59 60 61 #endif 62