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 different approach for solving the nonlinear Fredholm integral equations of the second kind. (English) Zbl 1092.65117

The authors discuss a method for finding an approximate solution of the nonlinear Fredholm integral equation of the second kind

x(t)=y(t)+ a b k(t,s,x(s))ds,a.e.on[a,b]

First, the problem under consideration is converted to an optimal control problem by introducing an artificial control function. Then a linear programming problem is formulated by using some concepts of measure theory. The solution of this linear programming problem provides the approximate solution of the Fredholm integral equation. It is shown that the nonlinearity of the kernel has no serious effect on the convergence of the solution. Some examples are given to illustrate the applicability of the method.

MSC:
65R20Integral equations (numerical methods)
45G10Nonsingular nonlinear integral equations
49J22Optimal control problems with integral equations (existence) (MSC2000)
90C05Linear programming