Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1234.65034
Su, Lijuan; Wang, Wenqia; Yang, Zhaoxia
Finite difference approximations for the fractional advection-diffusion equation. (English)
[J] Phys. Lett., A 373, No. 48, 4405-4408 (2009). ISSN 0375-9601

Summary: Fractional order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this Letter, in order to solve the two-sided fractional advection-diffusion equation, the fractional Crank-Nicholson method (FCN) is given, which is based on shifted Grünwald-Letnikov formula. It is shown that this method is unconditionally stable, consistent and convergent. The accuracy with respect to the time step is of order $(\Delta t)^2$. A numerical example is presented to confirm the conclusions.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
60G22
60J60 Diffusion processes
35K57 Reaction-diffusion equations
35R11

Keywords: two-sided fractional advection; diffusion equation; shifted Grünwald-Letnikov formula; Crank-Nicholson method; stability analysis

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]