\( D_{0} \) matricial representation More...
#include <ql/methods/finitedifferences/dzero.hpp>
 Inheritance diagram for DZero:
 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_ | 
| boost::shared_ptr< TimeSetter > | timeSetter_ | 
\( D_{0} \) matricial representation
The differential operator \( D_{0} \) discretizes the first derivative with the second-order formula
\[ \frac{\partial u_{i}}{\partial x} \approx \frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i} \]