Abstract: In this study, we examine some spectral properties
of non-selfadjoint matrix-valued difference equations consisting of
a polynomial-type Jost solution. The aim of this study is to
investigate the eigenvalues and spectral singularities of the difference
operator L which is expressed by the above-mentioned difference
equation. Firstly, thanks to the representation of polynomial type Jost
solution of this equation, we obtain asymptotics and some analytical
properties. Then, using the uniqueness theorems of analytic functions,
we guarantee that the operator L has a finite number of eigenvalues
and spectral singularities.
Abstract: This paper is concerned with the global asymptotic
behavior of positive solution for a system of two nonlinear rational
difference equations. Moreover, some numerical examples are given
to illustrate results obtained.
Abstract: In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.
Abstract: In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.
Abstract: A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.
Abstract: A novel PDE solver using the multidimensional wave
digital filtering (MDWDF) technique to achieve the solution of a 2D
seismic wave system is presented. In essence, the continuous physical
system served by a linear Kirchhoff circuit is transformed to an
equivalent discrete dynamic system implemented by a MD wave
digital filtering (MDWDF) circuit. This amounts to numerically
approximating the differential equations used to describe elements of a
MD passive electronic circuit by a grid-based difference equations
implemented by the so-called state quantities within the passive
MDWDF circuit. So the digital model can track the wave field on a
dense 3D grid of points. Details about how to transform the continuous
system into a desired discrete passive system are addressed. In
addition, initial and boundary conditions are properly embedded into
the MDWDF circuit in terms of state quantities. Graphic results have
clearly demonstrated some physical effects of seismic wave (P-wave
and S–wave) propagation including radiation, reflection, and
refraction from and across the hard boundaries. Comparison between
the MDWDF technique and the finite difference time domain (FDTD)
approach is also made in terms of the computational efficiency.
Abstract: This paper presents an improved image segmentation
model with edge preserving regularization based on the
piecewise-smooth Mumford-Shah functional. A level set formulation
is considered for the Mumford-Shah functional minimization in
segmentation, and the corresponding partial difference equations are
solved by the backward Euler discretization. Aiming at encouraging
edge preserving regularization, a new edge indicator function is
introduced at level set frame. In which all the grid points which is used
to locate the level set curve are considered to avoid blurring the edges
and a nonlinear smooth constraint function as regularization term is
applied to smooth the image in the isophote direction instead of the
gradient direction. In implementation, some strategies such as a new
scheme for extension of u+ and u- computation of the grid points and
speedup of the convergence are studied to improve the efficacy of the
algorithm. The resulting algorithm has been implemented and
compared with the previous methods, and has been proved efficiently
by several cases.
Abstract: In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Abstract: This paper reviews various approaches that have been
used for the modeling and simulation of large-scale engineering
systems and determines their appropriateness in the development of a
RICS modeling and simulation tool. Bond graphs, linear graphs,
block diagrams, differential and difference equations, modeling
languages, cellular automata and agents are reviewed. This tool
should be based on linear graph representation and supports symbolic
programming, functional programming, the development of noncausal
models and the incorporation of decentralized approaches.
Abstract: In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.