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)
A rational approximation and its applications to differential equations on the half line. (English) Zbl 0984.65104
The system of orthogonal rational functions induced by the Legendre polynomials and its basic properties are introduced. Various orthogonal projections are studied and established some results on rational approximation are established. Two kinds of rational interpolation are considered. A rational spectral method and a rational pseudospectral method for two model problems are analyzed. Finally, some numerical implementations and numerical results are presented which agree well with the theoretical analysis and which demonstrate the effectiveness of the considered approach.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
41A20Approximation by rational functions
34B05Linear boundary value problems for ODE
35K05Heat equation
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65D05Interpolation (numerical methods)