Second-order difference equations in diffraction theory
Article first published online: 7 DEC 2012
Copyright 2000 by the American Geophysical Union.
Volume 35, Issue 3, pages 683–690, May-June 2000
How to Cite
2000), Second-order difference equations in diffraction theory, Radio Sci., 35(3), 683–690, doi:10.1029/1999RS002246., and (
- Issue published online: 7 DEC 2012
- Article first published online: 7 DEC 2012
- Manuscript Accepted: 8 MAR 2000
- Manuscript Received: 18 AUG 1999
A technique is presented to solve a class of second-order functional difference equations that arise in diffraction theory. Branch-free solutions are obtained by linearly combining branched functions satisfying first-order equations derived from the second-order difference equation. The approach used is conceptually simple, and the underlying analysis is relatively straightforward. Analysis and computations both demonstrate that the resulting solutions have the desired analytical properties and recover the known expressions in the proper limit.