On the convergence of orthogonal eigenfunction series

John G. Fikioris

Mathematics and Computers in Simulation (MATCOM), 1985, vol. 27, issue 5, 531-539

Abstract: The method of Watson's Transformation, well known in high frequency scattering, is applied to a two-dimensional, orthogonal eigenfunction series of rectangular harmonic functions, which provides the solution to a typical boundary value problem of Laplace's equation. A new infinite, so-called residue, series is obtained exhibiting convergence properties stronger than, in certain respects, and complementary to the original eigenfunction series. Convergence of the two series and of their derivatives is further compared and tested near points of discontinuity. “Extraction” of the discontinuous term out of the original series and reexpansion of the solution provides a third eigenfunction series with uniform convergence in the whole region and good convergence near the singularities of the solution. Eigenfunction series of other boundary value problems are, also, discussed and similarities with the evaluation of complicated Fourier or Sommerfeld integrals via contour integration are pointed out.

Date: 1985
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378475485900722
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:27:y:1985:i:5:p:531-539

DOI: 10.1016/0378-4754(85)90072-2

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().