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 finite difference techniques for the one-dimensional advection-diffusion equation. (English) Zbl 1034.65069
Summary: Various numerical techniques are developed and compared for solving the one-dimensional advection–diffusion equation with constant coefficient. These techniques are based on the two-level finite difference approximations. The basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed by R. F. Warming and B. J. Hyett [J. Comput. Phys. 14, 159–179 (1974; Zbl 0291.65023)]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. The new methods are more accurate and are more efficient than the conventional techniques. These schemes are free of numerical diffusion. The results of a numerical experiment are presented, and the accuracy and central processor (CPU) time needed are discussed and compared.
MSC:
65M06Finite difference methods (IVP of PDE)
35K15Second order parabolic equations, initial value problems
65M12Stability and convergence of numerical methods (IVP of PDE)