کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
518748 867611 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain
چکیده انگلیسی

In this paper, for a class of fractional sub-diffusion equations on a space unbounded domain, firstly, exact artificial boundary conditions, which involve the time-fractional derivatives, are derived using the Laplace transform technique. Then the original problem on the space unbounded domain is reduced to the initial-boundary value problem on a space bounded domain. Secondly, an efficient finite difference approximation for the reduced initial-boundary problem on the space bounded domain is constructed. Different from the method of order reduction used in [37] for the fractional sub-diffusion equations on a space half-infinite domain, the presented difference scheme, which is more simple than that in the previous work, is developed using the direct discretization method, i.e. the approximate method of considering the governing equations at mesh points directly. The stability and convergence of the scheme with numerical accuracy O(τ2-γ+h2)O(τ2-γ+h2) are proved by means of discrete energy method and Sobolev imbedding inequality, where γ is the order of time-fractional derivative in the governing equation, τ and h   are the temporal stepsize and spatial stepsize, respectively. Thirdly, a compact difference scheme for the case of γ⩽2/3γ⩽2/3 is derived with the truncation errors of fourth-order accuracy for interior points and third-order accuracy for boundary points, respectively. Then the global convergence order O(τ2-γ+h4)O(τ2-γ+h4) of the compact difference scheme is proved. Finally, numerical experiments are used to verify the numerical accuracy and the efficiency of the obtained schemes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 236, 1 March 2013, Pages 443–460
نویسندگان
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