zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Weighted average finite difference methods for fractional diffusion equations. (English) Zbl 1094.65085
Summary: A class of finite difference methods for solving fractional diffusion equations is considered. These methods are an extension of the weighted average methods for ordinary (non-fractional) diffusion equations. Their accuracy is of order (Δx) 2 and Δt, except for the fractional version of the Crank-Nicolson method, where the accuracy with respect to the timestep is of order (Δt) 2 if a second-order approximation to the fractional time-derivative is used. Their stability is analyzed by means of a recently proposed procedure akin to the standard von Neumann stability analysis [S. B. Yuste and L. Acedo, SIAM J. Numer. Anal. 42, No. 5, 1862–1874 (2005; Zbl 1119.65379)]. A simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, is found and checked numerically. Some examples are provided in which the new methods’ numerical solutions are obtained and compared against exact solutions.
MSC:
65M06Finite difference methods (IVP of PDE)