Derivation of the solution of certain singular integral equations

Chakrabarti, Aloknath (1980) Derivation of the solution of certain singular integral equations. In: Journal Of The Indian Institute Of Science Section A-Engineering & Technology, 62 (10). pp. 147-157.

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Abstract

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Item Type:	Journal Article
Publication:	Journal Of The Indian Institute Of Science Section A-Engineering & Technology
Publisher:	J Indian Inst Science
Additional Information:	Copyright of this article belongs to Indian Inst Science.
Keywords:	Singular integral equations,Cauch typkee rnel, Riemann Hilbert prrblem,wawguidc them.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	10 Aug 2009 09:34
Last Modified:	19 Sep 2010 05:38
URI:	http://eprints.iisc.ac.in/id/eprint/21740

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