The paper is devoted to the foundation of
approximation methods for integral equations of
the form (aI+SbI+K)f=g,
where S is the Cauchy singular
integral operator on (-1,1) and K is a weakly
singular integral operator.
Here a,b,g are given functions on (-1,1) and
the unknown function f on (-1,1) is looked for.
It is assumed that a and b are real-valued and
Hölder continuous functions on [-1,1] without
common zeros and that g belongs to some
weighted space of Hölder continuous functions.
In particular, g may have a finite number of
singularities.
Based on known spectral properties of Cauchy
singular integral operators approximation methods
for the numerical solution of the above equation
are constructed, where both aspects the
theoretical convergence and the numerical
practicability are taken into account.
The weighted uniform convergence of these methods
is studied using a general
approach based on the theory of approximation
spaces. With the help of this approach it is
possible to prove simultaneously the stability,
the convergence and results on the order of
convergence of the approximation methods under
consideration.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200500895 |
| Date | 01 August 2005 |
| Creators | Luther, Uwe |
| Contributors | TU Chemnitz, Fakultät für Mathematik, Prof. Dr. Peter Junghanns, Prof. Dr. Jürgen Prestin, Prof. Dr. Maria Rosaria Capobianco |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
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