Solution of linear and nonlinear diffusion problems via stochastic differential equations

• Autorzy: Bargieł M. , Tory E. M.

Identyfikatory

DOI

10.7494/csci.2015.16.4.415

• Języki publikacji: EN

Abstrakty

EN

The equation for nonlinear diffusion can be rearranged to a form that immediately leads to its stochastic analog. The latter contains a drift term that is absent when the diffusion coefficient is constant. The dependence of this coefficient 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 diffusion problems with finite or infinite boundaries and for diffusion in cylindrical or spherical shells. By mimicking the movements of molecules, the stochastic 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.

Słowa kluczowe

EN

nonlinear diffusion; stochastic differential equations; Wiener process; Itô process; Kolmogorov backward equation

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2015
• Tom: Vol. 16 (4)
• Strony: 415--428
• Opis fizyczny: Bibliogr. 10 poz., rys., wykr., tab.

Twórcy

autor

Bargieł M.

• AGH University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Department of Computer Science, Krakow, Poland

autor

Tory E. M.

• Department of Mathematics and Computer Science, Mount Allison University, P.O. Box 6054, Sackville, NB, E4L 1G6, Canada

Bibliografia

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