## Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions

Publication
, Journal Article

Reif, J; Barakat, R

Published in: Journal of Computational Physics

January 1, 1977

Chebyschev approximations are employed to solve the one-dimensional, time-dependent Fokker-Planck (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 Ornstein-Uhlenbeck process for a variety of combinations of boundary conditions. © 1977.

### Duke Scholars

## Published In

Journal of Computational Physics

## DOI

## EISSN

1090-2716

## ISSN

0021-9991

## Publication Date

January 1, 1977

## Volume

23

## Issue

4

## Start / End Page

425 / 445

## Related Subject Headings

- Applied Mathematics
- 51 Physical sciences
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences
- 01 Mathematical Sciences

### Citation

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MLA

NLM

Reif, J., & Barakat, R. (1977). Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions.

*Journal of Computational Physics*,*23*(4), 425–445. https://doi.org/10.1016/0021-9991(77)90072-9Reif, J., and R. Barakat. “Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions.”

*Journal of Computational Physics*23, no. 4 (January 1, 1977): 425–45. https://doi.org/10.1016/0021-9991(77)90072-9.Reif J, Barakat R. Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions. Journal of Computational Physics. 1977 Jan 1;23(4):425–45.

Reif, J., and R. Barakat. “Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions.”

*Journal of Computational Physics*, vol. 23, no. 4, Jan. 1977, pp. 425–45.*Scopus*, doi:10.1016/0021-9991(77)90072-9.Reif J, Barakat R. Numerical solution of the Fokker-Planck equation via chebyschev polynomial approximations with reference to first passage time probability density functions. Journal of Computational Physics. 1977 Jan 1;23(4):425–445.

## Published In

Journal of Computational Physics

## DOI

## EISSN

1090-2716

## ISSN

0021-9991

## Publication Date

January 1, 1977

## Volume

23

## Issue

4

## Start / End Page

425 / 445

## Related Subject Headings

- Applied Mathematics
- 51 Physical sciences
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences
- 01 Mathematical Sciences