Package 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
    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 Details

    • 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.