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An approximation method using approximate approximations

dc.date.accessioned2006-04-06T11:39:17Z
dc.date.available2006-04-06T11:39:17Z
dc.date.issued2005
dc.identifier.uriurn:nbn:de:hebis:34-200604069104
dc.identifier.urihttp://hdl.handle.net/123456789/200604069104
dc.format.extent132946 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherUniversität Kassel, FB 17, Mathematik/Informatikeng
dc.rightsUrheberrechtlich geschützt
dc.rights.urihttps://rightsstatements.org/page/InC/1.0/
dc.subjectApproximate approximationseng
dc.subjectLaplace equationeng
dc.subjectDirichlet problemeng
dc.subjectBoundary integral equationeng
dc.subjectApproximationstheorieeng
dc.subjectLaplace-Gleichungeng
dc.subjectDirichlet-Problemeng
dc.subjectIntegralgleichungeng
dc.subject.ddc510
dc.titleAn approximation method using approximate approximationseng
dc.typePreprint
dcterms.abstractThe aim of this paper is to extend the method of approximate approximations to boundary value problems. This method was introduced by V. Maz'ya in 1991 and has been used until now for the approximation of smooth functions defined on the whole space and for the approximation of volume potentials. In the present paper we develop an approximation procedure for the solution of the interior Dirichlet problem for the Laplace equation in two dimensions using approximate approximations. The procedure is based on potential theoretical considerations in connection with a boundary integral equations method and consists of three approximation steps as follows. In a first step the unknown source density in the potential representation of the solution is replaced by approximate approximations. In a second step the decay behavior of the generating functions is used to gain a suitable approximation for the potential kernel, and in a third step Nyström's method leads to a linear algebraic system for the approximate source density. For every step a convergence analysis is established and corresponding error estimates are given.eng
dcterms.accessRightsopen access
dcterms.creatorMüller, Frank
dcterms.creatorVarnhorn, Werner
dcterms.isPartOfMathematische Schriften Kasseleng
dcterms.isPartOf05, 11eng
dc.subject.msc65N38eng
dc.subject.msc45B05eng
dc.subject.msc35J05eng
dcterms.source.journalMathematische Schriften Kassel
dcterms.source.volume05, 11


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