Class SpaceTimeDiscretization

java.lang.Object

net.finmath.finitedifference.grids.SpaceTimeDiscretization

public class SpaceTimeDiscretization
extends Object

Encapsulates the space-time discretization used in a finite difference scheme.

The class contains:

• A possibly multi-dimensional spatial grid, stored as a collection of Grid objects indexed by their dimension (index 0 corresponds to the one-dimensional case).
• A TimeDiscretization, interpreted as a discretization of time-to-maturity. In the finite difference framework, the PDE is solved backward in time, so 0 corresponds to maturity.
• The parameter theta, controlling the theta-method (explicit, implicit, or Crank–Nicolson).
• A center point per spatial dimension.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
SpaceTimeDiscretization(Grid[] spaceGrids, TimeDiscretization timeDiscretization, double theta, double[] center)	Constructs a multi-dimensional space-time discretization.
SpaceTimeDiscretization(Grid spaceGrid, TimeDiscretization timeDiscretization, double theta, double[] center)	Constructs a one-dimensional space-time discretization.

Method Summary

Modifier and Type	Method	Description
double[]	getCenter()	Returns the value.
double	getCenter(int dimension)	Returns the center coordinate for the specified spatial dimension.
int	getNumberOfSpaceGrids()	Returns the value.
Grid	getSpaceGrid(int dimension)	Returns the spatial grid corresponding to the given dimension.
HashMap<Integer,Grid>	getSpaceGrids()	Returns the value.
double	getTheta()	Returns the theta parameter of the theta-method.
TimeDiscretization	getTimeDiscretization()	Returns the time discretization.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

SpaceTimeDiscretization

public SpaceTimeDiscretization(Grid spaceGrid,
 TimeDiscretization timeDiscretization,
 double theta,
 double[] center)

Constructs a one-dimensional space-time discretization.

Parameters:

spaceGrid - The spatial grid.

timeDiscretization - The time discretization (time-to-maturity).

theta - The theta parameter of the theta-method.

center - The center point of the spatial grid.

SpaceTimeDiscretization

public SpaceTimeDiscretization(Grid[] spaceGrids,
 TimeDiscretization timeDiscretization,
 double theta,
 double[] center)

Constructs a multi-dimensional space-time discretization.

The i-th grid in the array is stored under key i.

Parameters:

spaceGrids - Array of grids, one per spatial dimension.

timeDiscretization - The time discretization (time-to-maturity).

theta - The theta parameter of the theta-method.

center - Center point per dimension (same length as spaceGrids).

Method Details

getSpaceGrids

public HashMap<Integer,Grid> getSpaceGrids()

Returns the value.

Returns:

The value.

getCenter

public double[] getCenter()

Returns the value.

Returns:

The value.

getSpaceGrid

public Grid getSpaceGrid(int dimension)

Returns the spatial grid corresponding to the given dimension.

Parameters:

dimension - The spatial dimension index.

Returns:

The corresponding Grid.

getTimeDiscretization

public TimeDiscretization getTimeDiscretization()

Returns the time discretization.

Returns:

The TimeDiscretization.

getTheta

public double getTheta()

Returns the theta parameter of the theta-method.

Returns:

The theta parameter.

getCenter

public double getCenter(int dimension)

Returns the center coordinate for the specified spatial dimension.

Parameters:

dimension - The spatial dimension index.

Returns:

The center value for the given dimension.

getNumberOfSpaceGrids

public int getNumberOfSpaceGrids()

Returns the value.

Returns:

The value.