On the oscillations appearing in numerical solutions of solvable and nonsolvable integral equations for thin-wire antennas

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dc.contributor.author Papakanellos, PJ en
dc.contributor.author Fikioris, G en
dc.contributor.author Michalopoulou, A en
dc.date.accessioned 2014-03-01T01:34:02Z
dc.date.available 2014-03-01T01:34:02Z
dc.date.issued 2010 en
dc.identifier.issn 0018-926X en
dc.identifier.uri http://hdl.handle.net/123456789/20653
dc.subject Antenna feeds en
dc.subject Antenna theory en
dc.subject Galerkin method en
dc.subject Integral equations en
dc.subject Wire antennas en
dc.subject.classification Engineering, Electrical & Electronic en
dc.subject.classification Telecommunications en
dc.subject.other Antenna feeds en
dc.subject.other Antenna theory en
dc.subject.other Basis functions en
dc.subject.other Exact solution en
dc.subject.other Ill posed en
dc.subject.other Method of auxiliary sources en
dc.subject.other Numerical solution en
dc.subject.other Sinusoidal currents en
dc.subject.other Thin-wire antennas en
dc.subject.other Two equation en
dc.subject.other Wire antennas en
dc.subject.other Antenna feeders en
dc.subject.other Galerkin methods en
dc.subject.other Integral equations en
dc.subject.other Wire en
dc.subject.other Antennas en
dc.title On the oscillations appearing in numerical solutions of solvable and nonsolvable integral equations for thin-wire antennas en
heal.type journalArticle en
heal.identifier.primary 10.1109/TAP.2010.2044319 en
heal.identifier.secondary http://dx.doi.org/10.1109/TAP.2010.2044319 en
heal.identifier.secondary 5422615 en
heal.language English en
heal.publicationDate 2010 en
heal.abstract Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usualHalln and Pocklingtonequations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picard's theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel. © 2006 IEEE. en
heal.journalName IEEE Transactions on Antennas and Propagation en
dc.identifier.doi 10.1109/TAP.2010.2044319 en
dc.identifier.isi ISI:000277339900022 en
dc.identifier.volume 58 en
dc.identifier.issue 5 en
dc.identifier.spage 1635 en
dc.identifier.epage 1644 en

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