Szczegóły publikacji
Opis bibliograficzny
Solution of linear and nonlinear diffusion problems via stochastic differential equations / Monika BARGIEŁ, Elmer M. Tory // Computer Science ; ISSN 1508-2806. — 2015 — vol. 16 no. 4, s. 415–428. — Bibliogr. s. 428, Abstr.
Autorzy (2)
- AGHDekster Monika
- Tory Elmer M.
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 95712 |
|---|---|
| Data dodania do BaDAP | 2016-02-03 |
| Tekst źródłowy | URL |
| DOI | 10.7494/csci.2015.16.4.415 |
| Rok publikacji | 2015 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Computer Science |
Abstract
The equation for nonlinear diffusion can be rearranged to a form that imme- diately leads to its stochastic analog. The latter contains a drift term that is absent when the diffusion coefficient is constant. The dependence of this coef- ficient on concentration (or temperature) is handled by generating many paths in parallel and approximating the derivative of concentration with respect to distance by the central difference. This method works for one-dimensional diffu- sion problems with finite or infinite boundaries and for diffusion in cylindrical or spherical shells. By mimicking the movements of molecules, the stochas- tic approach provides a deeper insight into the physical process. The parallel version of our algorithm is very efficient. The 99% confidence limits for the stochastic solution enclose the analytical solution so tightly that they cannot be shown graphically. This indicates that there is no systematic difference in the results for the two methods. Finally, we present a direct derivation of the stochastic method for cylindrical and spherical shells.