com.imsl.math

Interface FeynmanKac.Boundaries

Enclosing class:

FeynmanKac

public static interface FeynmanKac.Boundaries

Public interface for user supplied boundary coefficients and terminal condition the PDE must satisfy.

Method Summary

Modifier and Type	Method and Description
void	leftBoundaries(double time, double[][] coefficients) Returns the coefficient values of the left boundary conditions.
void	rightBoundaries(double time, double[][] coefficients) Returns the coefficient values of the right boundary conditions.
double	terminal(double z) Returns the terminal condition value.

Method Detail

leftBoundaries

void leftBoundaries(double time,
                    double[][] coefficients)

Returns the coefficient values of the left boundary conditions. There are numLeftBounds conditions specified at the left end, \(x_{\min}\). The left boundary conditions are $$ a_i(x,t)f+b_i(x,t)f_x+c_i(x,t)f_{xx} = d_i(x,t),\, x=x_{\min},\, 1 \le i \le \text{numLeftBounds}. $$

Time dependency of the boundary coefficients can be controlled via method setTimeDependence. Use of this method will usually yield a more efficient algorithm because some finite element matrices do not have to be reassembled for each t value.

Parameters:

time - a double, the time point at which the boundary coefficients are to be evaluated.

coefficients - an output double array of dimension numLeftBounds by 4 containing the computed boundary coefficient values. The coefficients are stored row-wise according to the matrix scheme $$ ( a_i(x_{\min},t), b_i(x_{\min},t),c_i(x_{\min},t), d_i(x_{\min},t) )_{1 \le i \le \text{numLeftBounds}}\,. $$

rightBoundaries

void rightBoundaries(double time,
                     double[][] coefficients)

Returns the coefficient values of the right boundary conditions. There are numRightBounds conditions specified at the right end, \(x_{\max}\). The right boundary conditions are $$ a_i(x,t)f+b_i(x,t)f_x+c_i(x,t)f_{xx} = d_i(x,t),\, x=x_{\max},\, 1 \le i \le \text{numRightBounds}. $$

Time dependency of the boundary coefficients can be controlled via method setTimeDependence. Use of this method will usually yield a more efficient algorithm because some finite element matrices do not have to be reassembled for each t value.

Parameters:

time - a double, the time point at which the boundary coefficients are to be evaluated.

coefficients - an output double array of dimension numRightBounds by 4, containing the computed boundary coefficient values. The coefficients are stored row-wise according to the matrix scheme $$ ( a_i(x_{\max},t), b_i(x_{\max},t),c_i(x_{\max},t), d_i(x_{\max},t) )_{1 \le i \le \text{numRightBounds}}\,. $$

terminal

double terminal(double z)

Returns the terminal condition value.

Parameters:

z - a double scalar, the point in x- direction, where the terminal condition is evaluated.

Returns:

a double scalar, the value of the terminal condition \(p(x)\) at point z.