A complex number q with 0 < |q| < 1 is fixed. By an analytic q-difference equation we mean an equation which can be represented by a matrix equation Y (z) = A(z)Y (qz) where A(z) is an invertible n× n-matrix with coefficients in the field K = C({z}) of the convergent Laurent series and where Y (z) is a vector of size n. The aim of this paper is to give an overview of our present knowledge of th...

Asymptotic properties of some non-linear difference equations are considered. AMS(1980) Subject Classification: 39A12, 45E99..

We shall develop here a galois theory for difference equations. In the PicardVessiot galois theory for differential equations, the basic objects of study are the Picard-Vessiot extension of a field and its associated galois group. Recall that a Picard-Vessiot extension of a differential field k is an extension K generated by a fundamental set of solutions of a linear differential equation and h...

Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a sys...

We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of ...