The Solution of Second-Order Functional Difference Equations

Author

Senior, T.B.A. ; Michielssen, E.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA

Volume

52

Issue

2

fYear

2010

fDate

4/1/2010 12:00:00 AM

Firstpage

10

Lastpage

18

Abstract

This paper reviews analytical and numerical techniques for solving second-order functional difference equations. A periodic multiplier aside, solutions to these equations can be expressed as linear combinations of two linearly independent particular solutions. One of these solutions can often be found either analytically, by exploiting a known relationship between both solutions, or numerically, by solving a simple integral equation. Knowledge of one particular solution permits construction of the second by solving a first-order functional difference equation.

Keywords

difference equations; functional equations; integral equations; analytical technique; first order functional difference equation; integral equation; linear combination; linearly independent particular solution; numerical technique; second order functional difference equations; Difference equations; Equations; Fourier transforms; Integral equations; Irrigation; Difference equations; Fourier transforms; mathematics;

fLanguage

English

Journal_Title

Antennas and Propagation Magazine, IEEE

Publisher

ieee

ISSN

1045-9243

Type

jour

DOI

10.1109/MAP.2010.5525560

Filename

5525560