Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1193.35243
Li, Xianjuan; Xu, Chuanju
A space-time spectral method for the time fractional diffusion equation. (English)
[J] SIAM J. Numer. Anal. 47, No. 3, 2108-2131 (2009). ISSN 0036-1429; ISSN 1095-7170/e

Summary: We consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a spectral method in both temporal and spatial discretizations for this equation. The convergence of the method is proven by providing a priori error estimate. Numerical tests are carried out to confirm the theoretical results. Thanks to the spectral accuracy in both space and time of the proposed method, the storage requirement due to the ``global time dependence" can be considerably relaxed, and therefore calculation of the long-time solution becomes possible.

MSC 2000:: *35R11
35S10 Initial value problems for pseudodifferential operators
65M70 Spectral, collocation and related methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: space-time spectral method; time fractional diffusion equation; error estimate

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]