JMSLTM Numerical Library 7.2.0
com.imsl.math

Interface FeynmanKac.ForcingTerm

• Enclosing class:
FeynmanKac

public static interface FeynmanKac.ForcingTerm
Public interface for non-zero forcing term in the Feynman-Kac equation.
• Method Summary

Methods
Modifier and Type Method and Description
void force(int interval, double[] y, double time, double width, double[] xlocal, double[] qw, double[][] u, double[] phi, double[][] dphi)
Computes approximations to the forcing term and its derivative .
• Method Detail

• force

void force(int interval,
double[] y,
double time,
double width,
double[] xlocal,
double[] qw,
double[][] u,
double[] phi,
double[][] dphi)
Computes approximations to the forcing term and its derivative .
Parameters:
interval - an int, the index related to the integration interval [xGrid[interval-1], xGrid[interval]].
y - an input double array of length 3*xGrid.length containing the coefficients of the Hermite quintic spline representing the solution of the Feynman-Kac equation at time point time. For each

the approximate solution is locally defined by

The values are stored as successive triplets in y.
time - a double, the time point.
width - a double, the width of the integration interval, width=xGrid[interval]-xGrid[interval-1].
xlocal - an input double array containing the Gauss-Legendre points translated and normalized to the interval [xGrid[interval-1], xGrid[interval]].
qw - an input double array containing the Gauss-Legendre weights.
u - an input double array of dimension 12 by xlocal.length containing the basis function values that define at the Gauss-Legendre points xlocal. Setting

vector is defined as

phi - an output double array of length 6 containing Gauss-Legendre approximations for the local contributions

where t=time and Denoting by degree the number of Gauss-Legendre points (xlocal.length) and setting , vector phi contains elements

for i=0,...,5.
dphi - an output double array of dimension 6 by 6 containing a Gauss-Legendre approximation for the Jacobian of the local contributions at time point t=time,

The approximation to this symmetric matrix is stored row-wise, i.e.

for i,j=0,...,5.
JMSLTM Numerical Library 7.2.0