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)
Numerical solution of the stationary FPK equation using Shannon wavelets. (English) Zbl 1237.65150
Summary: The Fokker-Planck-Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or non-linear system to random excitation. This paper proposes a numerical method for calculating the stationary solution of the FPK equation, which is based upon the weighted residual approach using Shannon wavelets as shape functions. The method is developed here for an n -dimensional system and its relationship with the distributed approximating functional (DAF) approach is investigated. For the purposes of validation, numerical results obtained using the proposed method are compared with available exact solutions and numerical solutions for some non-linear oscillators. For the systems considered excellent results over the main body and tails of the marginal distributions are obtained. The accuracy and efficiency of the method are investigated in comparison to the finite element method (FEM).
MSC:
65T60Wavelets (numerical methods)
65C20Models (numerical methods)
34F05ODE with randomness
70L05Random vibrations (general mechanics)
82C80Numerical methods of time-dependent statistical mechanics