Approximation of Solutions to Nonautonomous Difference Equations

Strictly Increasing Solutions of Nonautonomous Difference Equations Arising in Hydrodynamics

The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation x n 1 x n n/ n 1 2 x n − x n − 1 h2f x n , n ∈ N, where h > 0 is a parameter and f is Lipschitz continuous and has three real zeros L0 < 0 < L. In particular we prove that for each sufficiently small h > 0 there exists a solution {x n }n 0 such that {...

Asymptotic Properties of Solutions of Nonautonomous Difference Equations

Asymptotic properties of solutions of difference equation of the form ∆xn = anφn(xσ(n)) + bn are studied. Conditions under which every (every bounded) solution of the equation ∆yn = bn is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than m is asymptotically equivalent to some solution...

Nonautonomous difference equations: Open problems and conjectures

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

Periodicity Detection in Nonautonomous Difference Equations

System identification for nonlinear differential and difference equations has lagged far behind the linear case, due to the greater complexity of the task. Takens’ Theorem [1,10] of 25 years ago opened a new avenue of investigation, introducing geometric methods that were essential for nonlinear problems. The ramifications of this result have unfolded in an area that has become known as attract...