**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2630

# Search results for: approximate solution.

##### 2630 An Approximate Solution of the Classical Van der Pol Oscillator Coupled Gyroscopically to a Linear Oscillator Using Parameter-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Samad Kheybari

**Abstract:**

In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.

**Keywords:**
Parameter-expansion method,
classical Van der Pol oscillator.

##### 2629 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 2628 APPLE: Providing Absolute and Proportional Throughput Guarantees in Wireless LANs

**Authors:**
Zhijie Ma,
Qinglin Zhao,
Hongning Dai,
Huan Zhang

**Abstract:**

**Keywords:**
IEEE 802.11e,
throughput guarantee,
priority.

##### 2627 Heat Transfer of an Impinging Jet on a Plane Surface

**Authors:**
Jian-Jun Shu

**Abstract:**

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.

**Keywords:**
Flux,
free impinging jet,
solid-surface,
uniform wall
temperature.

##### 2626 On the Solution of Fully Fuzzy Linear Systems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

**Keywords:**
Fully fuzzy linear equations,
iterative method,
homotopy perturbation method,
approximate solutions.

##### 2625 Approximate Solution of Some Mixed Boundary Value Problems of the Generalized Theory of Couple-Stress Thermo-Elasticity

**Authors:**
M. Chumburidze,
D. Lekveishvili

**Abstract:**

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

**Keywords:**
The couple-stress thermo-elasticity,
boundary value problems.

##### 2624 Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs

**Authors:**
A. A. James,
A. O. Adesanya,
M. R. Odekunle,
D. G. Yakubu

**Abstract:**

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

**Keywords:**
Interpolation,
Approximate Solution,
Collocation,
Differential system,
Half step,
Converges,
Block method,
Efficiency.

##### 2623 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

**Authors:**
M. A. Koroma,
C. Zhan,
A. F. Kamara,
A. B. Sesay

**Abstract:**

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

**Keywords:**
Laplace decomposition,
pantograph equations,
exact
solution,
numerical solution,
approximate solution.

##### 2622 Approximately Jordan Maps and Their Stability

**Authors:**
Nasrin Eghbali

**Abstract:**

In this paper we consider the approximate Jordan maps and boundedness of these maps. Also we investigate the stability of approximate Jordan maps and prove some stability properties for approximate Jordan maps.

**Keywords:**
Approximate Jordan map,
stability.

##### 2621 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.

##### 2620 Analytical Based Truncation Principle of Higher-Order Solution for a x1/3 Force Nonlinear Oscillator

**Authors:**
Md. Alal Hosen

**Abstract:**

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^{1/3}. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^{1/3} force nonlinear oscillator but it is also useful for many other nonlinear problems.

**Keywords:**
Approximate solutions,
Harmonic balance method,
Nonlinear oscillator,
Perturbation.

##### 2619 Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method

**Authors:**
Emad K. Jaradat,
Ala’a Al-Faqih

**Abstract:**

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

**Keywords:**
Non-linear Schrodinger equation,
Elzaki decomposition method,
harmonic oscillator,
one and two- dimensional Schrodinger equation.

##### 2618 Approximation Algorithm for the Shortest Approximate Common Superstring Problem

**Authors:**
A.S. Rebaï,
M. Elloumi

**Abstract:**

**Keywords:**
Shortest approximate common superstring,
approximation algorithms,
strings overlaps,
complexities.

##### 2617 Numerical Approximation to the Performance of CUSUM Charts for EMA (1) Process

**Authors:**
K. Petcharat,
Y. Areepong,
S. Sukparungsri,
G. Mititelu

**Abstract:**

**Keywords:**
Cumulative Sum Chart,
Moving Average
Observation,
Average Run Length,
Numerical Approximations.

##### 2616 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

**Authors:**
Saeideh Hesam,
Alireza Nazemi,
Ahmad Haghbin

**Abstract:**

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

**Keywords:**
Zakharov-Kuznetsov equation,
differential transform method,
closed form solution.

##### 2615 A Special Algorithm to Approximate the Square Root of Positive Integer

**Authors:**
Hsian Ming Goo

**Abstract:**

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

**Keywords:**
Special approximate algorithm,
square root,
Pell’s
equation,
Newton’s method,
error analysis.

##### 2614 Application of He’s Parameter-Expansion Method to a Coupled Van Der Pol oscillators with Two Kinds of Time-delay Coupling

**Authors:**
Mohammad Taghi Darvishi,
Samad Kheybari

**Abstract:**

In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.

**Keywords:**
Parameter-expansion method,
coupled van der pol oscillator,
time-delay system.

##### 2613 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 2612 Optimal Control Problem, Quasi-Assignment Problem and Genetic Algorithm

**Authors:**
Omid S. Fard,
Akbar H. Borzabadi

**Abstract:**

**Keywords:**
Optimal control,
Integer programming,
Genetic algorithm,
Discrete approximation,
Linear programming.

##### 2611 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

**Authors:**
M. Abdulkawi,
Z. K. Eshkuvatov,
N. M. A. Nik Long

**Abstract:**

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

**Keywords:**
Singular integral equations,
Cauchy kernel,
Chebyshev polynomials,
interpolation.

##### 2610 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

**Authors:**
Akbar H. Borzabadi,
Omid S. Fard

**Abstract:**

**Keywords:**
Fredholm integral equation,
Optimization method,
Optimal control,
Nonlinear and linear programming

##### 2609 Approximate Frequent Pattern Discovery Over Data Stream

**Authors:**
Kittisak Kerdprasop,
Nittaya Kerdprasop

**Abstract:**

**Keywords:**
Frequent pattern discovery,
Approximate algorithm,
Data stream analysis.

##### 2608 More on Gaussian Quadratures for Fuzzy Functions

**Authors:**
Shu-Xin Miao

**Abstract:**

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

**Keywords:**
Guassian quadrature rules,
fuzzy number,
fuzzy integral,
fuzzy solution.

##### 2607 Unique Positive Solution of Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Fengxia Zheng

**Abstract:**

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

**Keywords:**
Fractional differential equation,
boundary value problem,
positive solution,
existence and uniqueness,
fixed point theorem,
mixed monotone operator.

##### 2606 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations

**Authors:**
Jinfeng Wang,
Yang Liu,
Hong Li

**Abstract:**

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

**Keywords:**
Hyperbolic wave equation,
Nonlinear,
He’s variational
iteration method,
Transformations

##### 2605 Trajectory-Based Modified Policy Iteration

**Abstract:**

**Keywords:**
Markov Decision Process (MDP),
Mobile robot,
Policy iteration,
Simulation.

##### 2604 Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices

**Authors:**
Khosrow Maleknejad,
Yaser Rostami

**Abstract:**

In this paper, Semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions

**Keywords:**
Integro-differential equations,
Quartic B-spline
wavelet,
Operational matrices.

##### 2603 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev

**Abstract:**

**Keywords:**
Homotopy perturbation method,
Padé approximants,
cubic Boussinesq equation,
modified Boussinesq equation.

##### 2602 Finding Approximate Tandem Repeats with the Burrows-Wheeler Transform

**Authors:**
Agnieszka Danek,
Rafał Pokrzywa

**Abstract:**

**Keywords:**
approximate tandem repeats,
Burrows-Wheeler transform,
Hamming distance,
suffix array

##### 2601 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
Fengxia Zheng,
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
Boundary value
problem,
Positive solution,
Existence and uniqueness,
Fixed point
theorem of a sum operator.