**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2252

# Search results for: Difference equations

##### 2252 On the System of Nonlinear Rational Difference Equations

**Authors:**
Qianhong Zhang,
Wenzhuan Zhang

**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.

**Keywords:**
Difference equations,
stability,
unstable,
global
asymptotic behavior.

##### 2251 Matrix Valued Difference Equations with Spectral Singularities

**Authors:**
Serifenur Cebesoy,
Yelda Aygar,
Elgiz Bairamov

**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.

**Keywords:**
Difference Equations,
Jost Functions,
Asymptotics,
Eigenvalues,
Continuous Spectrum,
Spectral Singularities.

##### 2250 Applications of High-Order Compact Finite Difference Scheme to Nonlinear Goursat Problems

**Authors:**
Mohd Agos Salim Nasir,
Ahmad Izani Md. Ismail

**Abstract:**

**Keywords:**
Goursat problem,
partial differential equation,
finite
difference scheme,
compact finite difference

##### 2249 A Fully Implicit Finite-Difference Solution to One Dimensional Coupled Nonlinear Burgers’ Equations

**Authors:**
Vineet K. Srivastava,
Mukesh K. Awasthi,
Mohammad Tamsir

**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.

**Keywords:**
Burgers’ equation,
Implicit Finite-difference method,
Newton’s method,
Gauss elimination with partial pivoting.

##### 2248 A Finite Difference Calculation Procedure for the Navier-Stokes Equations on a Staggered Curvilinear Grid

**Authors:**
R. M. Barron,
B. Zogheib

**Abstract:**

**Keywords:**
Curvilinear,
finite difference,
finite volume,
SIMPLE.

##### 2247 Application of the Central-Difference with Half- Sweep Gauss-Seidel Method for Solving First Order Linear Fredholm Integro-Differential Equations

**Authors:**
E. Aruchunan,
J. Sulaiman

**Abstract:**

**Keywords:**
Integro-differential equations,
Linear fredholm
equations,
Finite difference,
Quadrature formulas,
Half-Sweep
iteration.

##### 2246 Electromagnetic Wave Propagation Equations in 2D by Finite Difference Method

**Authors:**
N. Fusun Oyman Serteller

**Abstract:**

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples. Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

**Keywords:**
Finite difference method,
finite element method,
linear-nonlinear PDEs,
symbolic computation,
wave propagation equations.

##### 2245 Stepsize Control of the Finite Difference Method for Solving Ordinary Differential Equations

**Authors:**
Davod Khojasteh Salkuyeh

**Abstract:**

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.

**Keywords:**
Ordinary differential equations,
optimal stepsize,
error,
stochastic arithmetic,
CESTAC,
CADNA.

##### 2244 Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales

**Authors:**
Changjin Xu,
Qianhong Zhang

**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.

**Keywords:**
Time scales,
competitive system,
periodic solution,
coincidence degree,
topological degree.

##### 2243 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

**Authors:**
J. Sulaiman,
M. Othman,
M. K. Hasan

**Abstract:**

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

**Keywords:**
MEG iteration,
second-order finite difference,
weighted parameter.

##### 2242 Development of Variable Stepsize Variable Order Block Method in Divided Difference Form for the Numerical Solution of Delay Differential Equations

**Authors:**
Fuziyah Ishak,
Mohamed B. Suleiman,
Zanariah A. Majid,
Khairil I. Othman

**Abstract:**

**Keywords:**
block method,
delay differential equations,
predictor-corrector,
stability region,
variable stepsize variable order.

##### 2241 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

**Authors:**
Jyh-Yang Wu,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Conservation laws,
diffusion equations,
Cahn-Hilliard Equations,
evolving surfaces.

##### 2240 On the Fuzzy Difference Equation xn+1 = A +

**Authors:**
Qianhong Zhang,
Lihui Yang,
Daixi Liao,

**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, · · ·}.

**Keywords:**
Fuzzy difference equation,
boundedness,
persistence,
equilibrium point,
asymptotic behaviour.

##### 2239 Dynamic Response of Strain Rate Dependent Glass/Epoxy Composite Beams Using Finite Difference Method

**Authors:**
M. M. Shokrieh,
A. Karamnejad

**Abstract:**

**Keywords:**
Composite beam,
Finite difference method,
Progressive damage modeling,
Strain rate.

##### 2238 Integral Image-Based Differential Filters

**Authors:**
Kohei Inoue,
Kenji Hara,
Kiichi Urahama

**Abstract:**

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

**Keywords:**
Integral images,
differential images,
differential filters,
image fusion.

##### 2237 A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

**Keywords:**
Curved stretching sheet,
finite difference method,
MHD,
variable thermal conductivity.

##### 2236 Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation

**Authors:**
M.Imanova,
G.Mehdiyeva,
V.Ibrahimov

**Abstract:**

**Keywords:**
Volterra integro-differential equations,
multistepmethods,
finite-difference methods,
initial value problem

##### 2235 On a New Nonlinear Sum-difference Inequality with Application

**Authors:**
Kelong Zheng,
Shouming Zhong

**Abstract:**

**Keywords:**
Sum-Difference inequality,
Nonlinear,
Boundedness.

##### 2234 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

**Authors:**
F. Rezaie Moghaddam,
J. Amani,
T. Rezaie Moghaddam

**Abstract:**

**Keywords:**
Heat conduction,
Cellular automata,
convergencerate,
discrete system.

##### 2233 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

**Keywords:**
Electromagnetism,
Maxwell's Equations,
Anisotropic permittivity,
Wave equation,
Matrix Equation,
Permittivity tensor.

##### 2232 A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces

**Authors:**
Mei-Hsiu Chi,
Jyh-Yang Wu,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Close surfaces,
high-order approach,
numerical solutions,
reaction-diffusion systems.

##### 2231 Simulation of Lightning Surge Propagation in Transmission Lines Using the FDTD Method

**Authors:**
Kokiat Aodsup,
Thanatchai Kulworawanichpong

**Abstract:**

**Keywords:**
Traveling wave,
Lightning surge,
Bewley lattice diagram,
Telegraphist's equations,
Finite-difference time-domain (FDTD) method,

##### 2230 The Comparison of Finite Difference Methods for Radiation Diffusion Equations

**Authors:**
Ren Jian,
Yang Shulin

**Abstract:**

**Keywords:**
Alternating Direction Method,
Non-SplittingMethod,
Radiation Diffusion.

##### 2229 Application of the Hybrid Methods to Solving Volterra Integro-Differential Equations

**Authors:**
G.Mehdiyeva,
M.Imanova,
V.Ibrahimov

**Abstract:**

**Keywords:**
Integro-differential equations,
initial value
problem,
hybrid methods,
predictor-corrector method

##### 2228 New Insight into Fluid Mechanics of Lorenz Equations

**Authors:**
Yu-Kai Ting,
Jia-Ying Tu,
Chung-Chun Hsiao

**Abstract:**

New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.

**Keywords:**
Galerkin method,
Lorenz equations,
Navier-Stokes
equations.

##### 2227 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

**Authors:**
N. Parandin,
M. A. Fariborzi Araghi

**Abstract:**

**Keywords:**
Fuzzy function integral equations,
Iterative method,
Linear systems,
Parametric form of fuzzy number.

##### 2226 An Efficient Backward Semi-Lagrangian Scheme for Nonlinear Advection-Diffusion Equation

**Authors:**
Soyoon Bak,
Sunyoung Bu,
Philsu Kim

**Abstract:**

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

**Keywords:**
Semi-Lagrangian method,
Iteration free method,
Nonlinear advection-diffusion equation.

##### 2225 A First Course in Numerical Methods with “Mathematica“

**Authors:**
Andrei A. Kolyshkin

**Abstract:**

**Keywords:**
Numerical methods,
"Mathematica",
e-learning.

##### 2224 An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations

**Authors:**
Gholamreza Hojjati,
Kourosh Parand

**Abstract:**

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

**Keywords:**
Lane-Emden type equations,
nonlinear ODE,
stiff problems,
multistep methods,
astrophysics.

##### 2223 Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides

**Authors:**
Leila Motamed-Jahromi,
Mohsen Hatami,
Alireza Keshavarz

**Abstract:**

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As_{2}S_{3} chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

**Keywords:**
Nonlinear optics,
propagation equation,
plasmonic waveguide.