Advances in Difference Equations
Volume 2010 (2010), Article ID 947058, 22 pages
Research Article

Transformations of Difference Equations I

School of Mathematics, University of the Witwatersrand, Private Bag 3, PO WITS 2050, Johannesburg, South Africa

Received 13 April 2010; Revised 27 July 2010; Accepted 29 July 2010

Academic Editor: Mariella Cecchi

Copyright © 2010 Sonja Currie and Anne D. Love. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a general weighted second-order difference equation. Two transformations are studied which transform the given equation into another weighted second order difference equation of the same type, these are based on the Crum transformation. We also show how Dirichlet and non-Dirichlet boundary conditions transform as well as how the spectra and norming constants are affected.