Skip Navigation



IMA Journal of Applied Mathematics Advance Access published online on July 26, 2007
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxm021
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
72/6/681    most recent
hxm021v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Antipov, Y.
Right arrow Articles by Silvestrov, V.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Method of integral equations for systems of difference equations in diffraction theory

YA Antipov{dagger}

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

VV Silvestrov{ddagger}

Department of Mathematics, Gubkin Russian State University of Oil and Gas, Moscow 119991, Russia

{dagger} Email: antipov{at}math.lsu.edu

{ddagger} Email: v_silvestrov{at}mail.ru

Received on April 4, 2006; Accepted on May 8, 2007

A system of difference equations of the first order with meromorphic coefficients (not necessary periodic ones) subject to certain conditions of symmetry is analysed. These conditions arise in model problems of diffraction theory. A method for the constructive solution of the system of difference equations is proposed. It consists of three steps. First, it requires factorization of a certain function. Then, scalar integral equations with the same kernel and different right-hand sides should be solved. The kernel of the equations has a fixed singularity, and the solution belongs to a class of functions with a power singularity. Finally, arbitrary constants are fixed from some conditions which guarantee the equivalence of the original system of difference equations and the integral equations. The method is illustrated by solving a model electromagnetic problem of a plane wave diffracted from an anisotropic impedance half-plane at oblique incidence.

Keywords: system of difference equations; Riemann-Hilbert problem; integral equation; electromagnetic diffraction.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.