IJPAM: Volume 47, No. 2 (2008)

REDUCTION OF ORDER OF SEPARABLE SECOND
ORDER DIFFERENCE EQUATIONS WITH
FORM SYMMETRIES

H. Sedaghat
Department of Mathematics and Applied Mathematics
College of Humanities and Science
Virginia Commonwealth University
1001 West Main Street, Oliver Hall, Rm. 2036C
P.O. Box 842014, Richmond, Virginia 23284-2014, USA
e-mail: hsedagha@vcu.edu


Abstract.By identifying form symmetries of a second order difference equation and substituting new variables for them we can reduce the order of the equation. We give a procedure based on solving a partial differential equation and apply this method to separable equations of type $x_{n+1}=\alpha_{n}\phi(x_{n})\psi(x_{n-1})$.

Received: May 12, 2008

AMS Subject Classification: 39A10, 39A20, 39B12

Key Words and Phrases: order reduction, form symmetry, semiconjugate, separable difference equation, partial differential equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 47
Issue: 2