On the application of numerical methods to Hallén's equation

Fikioris, G; Wu, TT

dc.contributor.author	Fikioris, G	en
dc.contributor.author	Wu, TT	en
dc.date.accessioned	2014-03-01T01:16:50Z
dc.date.available	2014-03-01T01:16:50Z
dc.date.issued	2001	en
dc.identifier.issn	0018-926X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14250
dc.subject	Galerkin's method	en
dc.subject	Integral equation methods	en
dc.subject	Wire antennas	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	Pulse functions	en
dc.subject.other	Electric currents	en
dc.subject.other	Galerkin methods	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Numerical methods	en
dc.subject.other	Antennas	en
dc.title	On the application of numerical methods to Hallén's equation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/8.918612	en
heal.identifier.secondary	http://dx.doi.org/10.1109/8.918612	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	The so-called Hallén integral equation for the current on a finite linear antenna center-driven by a delta-function generator takes two forms depending on the choice of kernel. The two kernels are usually referred to as the exact and the approximate or reduced kernel. With the approximate kernel, the integral equation has no solution. Nevertheless, the same numerical method is often applied to both forms of the integral equation. In this paper, the behavior of the numerical solutions thus obtained is investigated, and the similarities and differences between the two numerical solutions are discussed. The numerical method is Galerkin's method with pulse functions. We first apply this method to the two corresponding forms of the integral equation for the current on a linear antenna of infinite length. In this case, the method yields an infinite Toeplitz system of algebraic equations in which the width of the pulse basis functions enters as a parameter. The infinite system is solved exactly for nonzero pulse width; the exact solution is then developed asymptotically for the case where the pulse width is small. When the asymptotic expressions for the case of the infinite antenna are used as a guide for the behavior of the solutions of the finite antenna, the latter problem is greatly facilitated. For the approximate kernel, the main results of this paper carry over to a certain numerical method applied to the corresponding equation of the Pocklington type.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE Transactions on Antennas and Propagation	en
dc.identifier.doi	10.1109/8.918612	en
dc.identifier.isi	ISI:000168358100009	en
dc.identifier.volume	49	en
dc.identifier.issue	3	en
dc.identifier.spage	383	en
dc.identifier.epage	392	en