کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4642484 1341345 2007 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convergence of the Grünwald–Letnikov scheme for time-fractional diffusion
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Convergence of the Grünwald–Letnikov scheme for time-fractional diffusion
چکیده انگلیسی

Using bivariate generating functions, we prove convergence of the Grünwald–Letnikov difference scheme for the fractional diffusion equation (in one space dimension) with and without central linear drift in the Fourier–Laplace domain as the space and time steps tend to zero in a well-scaled way. This implies convergence in distribution (weak convergence) of the discrete solution towards the probability of sojourn of a diffusing particle. The difference schemes allow also interpretation as discrete random walks. For fractional diffusion with central linear drift we show that in the Fourier–Laplace domain the limiting ordinary differential equation coincides with that for the solution of the corresponding diffusion equation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 205, Issue 2, 15 August 2007, Pages 871–881
نویسندگان
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