Numerical solution of the FokkerPlanck equation via chebyschev polynomial approximations with reference to first passage time probability density functions
Abstract
Chebyschev approximations are employed to solve the onedimensional, timedependent FokkerPlanck (forward Kolmogrov) equation in the presence of two barriers a finite "distance" apart. Solutions are presented for the fundamental intervals (1, +1) and (0, +1). In order to speed up the calculations, sparse matrix routines are utilized. The first passage time probability density function is also evaluated. Illustrative numerical results are presented for the Wiener process with drift, and the OrnsteinUhlenbeck process for a variety of combinations of boundary conditions.
 Publication:

Journal of Computational Physics
 Pub Date:
 April 1977
 DOI:
 10.1016/00219991(77)900729
 Bibcode:
 1977JCoPh..23..425R