Analysis of a Discrete non-Markovian Random Walk Approximation for the Time Fractional Diffusion Equation
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Description
The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order in (0,1). In this work, an explicit finite-difference scheme for TFDE is presented. Discrete models of a non-Markovian random walk are generated for simulating random processes whose spatial probability density evolves in time according to this fractional diffusion equation. We derive the scaling restriction of the stability and convergence of the discrete non-Markovian random walk approximation for TFDE in a bounded domain. Finally, some numerical examples are presented to show the application of the present technique.
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| ID Code: | 22160 | ||||||
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| Item Type: | Contribution to Journal (Journal Article) | ||||||
| Refereed: | Yes | ||||||
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| Measurements or Duration: | 17 pages | ||||||
| ISSN: | 1446-1811 | ||||||
| Pure ID: | 34210512 | ||||||
| Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
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| Copyright Owner: | Copyright 2005 Australian Mathematical Society | ||||||
| Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||||||
| Deposited On: | 17 Jun 2009 13:06 | ||||||
| Last Modified: | 22 Jun 2024 18:42 |
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