Rational solutions of linear difference equations

Programming and Computer …, 2011

Complexities of some well known algorithms for finding rational solutions of linear difference equations with polynomial coefficients are studied.

Programming and Computer Software, 2012

An algorithm for finding a universal denominator of rational solutions of a system of linear differ ence equations with polynomial coefficients is proposed. The equations may have arbitrary orders.

Applied Mathematics and Computation, 2006

We find conditions for the global asymptotic stability of the unique negative equilibrium y ¼ 1 þ A of the equation

Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98, 1998

We propose an algorithm to compute rational function solutions for a first order system of linear difference equations with rational coefficients. This algorithm does not require preliminary uncoupling of the given system.

In this paper, we deal with the periodic nature and the form of the solutions of the following systems of rational difference equations x n+1 = x n−1 ±x n−1 y n − g , y n+1 = y n−1 ±y n−1 x n − f , with a nonzero real numbers initial conditions and f, g are nonzero real numbers with f, g 6 = 1.

Discrete Dynamics in Nature and Society, 2013

We deal with the form of the solutions for the following systems of rational difference equations +1 = (−1 /(± −1 ± −2)), +1 = (−1 /(± −1 ± −2)), with nonzero real numbers initial conditions. Also we investigate some properties of the obtained solutions and present some numerical examples.

ACM SIGSAM Bulletin, 2011

Some changes of the traditional scheme for finding rational solutions of linear differential, difference and q-difference homogeneous equations with rational coefficients are proposed. In many cases these changes allow one to predict the absence of rational solutions in an early stage of the computation.

Computers & Mathematics with Applications, 2001

We investigate the boundedness character, the periodic nature, and the global asymptotic stability of all positive solutions of the equation in the title with positive parameters and nonnegative initial conditions. (~

Journal of Nonlinear Sciences and Applications, 2018

In this paper, we examine and explore the boundedness, periodicity, and global stability of the positive solutions of the rational difference equation y n+1 = α

Journal of Mathematics, 2020

In this article, we discuss the problem about the properties on solutions for several types of q-difference equations and obtain some results on the exceptional values of transcendental meromorphic solutions fz with zero order, their q-differences Δqfz=fqz−fz, and divided differences Δqfz/fz. In addition, we also investigated the condition on the existence of rational solution for a class of q-difference equations. Our theorems are some extensions and supplement to those results given by Liu and Zhang and Qi and Yang.