کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10357170 | 867852 | 2005 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The accuracy and stability of an implicit solution method for the fractional diffusion equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The accuracy and stability of an implicit solution method for the fractional diffusion equation The accuracy and stability of an implicit solution method for the fractional diffusion equation](/preview/png/10357170.png)
چکیده انگلیسی
We have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. The implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement. The accuracy of the scheme is O(Îx2) in the spatial grid size and O(Ît1 + γ) in the fractional time step, where 0 ⩽ 1 â γ < 1 is the order of the fractional derivative and γ = 1 is standard diffusion. We have provided algebraic and numerical evidence that the scheme is unconditionally stable for 0 < γ ⩽ 1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 205, Issue 2, 20 May 2005, Pages 719-736
Journal: Journal of Computational Physics - Volume 205, Issue 2, 20 May 2005, Pages 719-736
نویسندگان
T.A.M. Langlands, B.I. Henry,