**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**356

# Search results for: Cairns-Gurevich Equation

##### 356 Stability of Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

**Keywords:**
Fractional calculus,
fractional differential equation,
Lane-Emden equation,
Riemann-Liouville fractional operators,
Volterra integral equation.

##### 355 Existence of Iterative Cauchy Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

**Keywords:**
Fractional calculus,
fractional differential equation,
Cauchy equation,
Riemann-Liouville fractional operators,
Volterra
integral equation,
non-expansive mapping,
iterative differential equation.

##### 354 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 353 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

**Keywords:**
Diophantine equation,
Pell equation,
quadratic form.

##### 352 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.

##### 351 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 350 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 349 Evolutionary Computation Technique for Solving Riccati Differential Equation of Arbitrary Order

**Authors:**
Raja Muhammad Asif Zahoor,
Junaid Ali Khan,
I. M. Qureshi

**Abstract:**

**Keywords:**
Riccati Equation,
Non linear ODE,
Fractional differential equation,
Genetic algorithm.

##### 348 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method

**Authors:**
Nisha Goyal,
R.K. Gupta

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

**Keywords:**
Sawada-Kotera-Kadomtsev-Petviashivili equation,
Bogoyavlensky-Konoplechenko equation,

##### 347 Performances Analysis of the Pressure and Production of an Oil Zone by Simulation of the Flow of a Fluid through the Porous Media

**Authors:**
Makhlouf Mourad,
Medkour Mihoub,
Bouchher Omar,
Messabih Sidi Mohamed,
Benrachedi Khaled

**Abstract:**

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

**Keywords:**
Darcy equation,
middle porous,
continuity equation,
Peng Robinson equation,
mobility.

##### 346 The Pell Equation x2 − (k2 − k)y2 = 2t

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Pell equation,
solutions of Pell equation.

##### 345 Lagrange-s Inversion Theorem and Infiltration

**Authors:**
Pushpa N. Rathie,
Prabhata K. Swamee,
André L. B. Cavalcante,
Luan Carlos de S. M. Ozelim

**Abstract:**

**Keywords:**
Green-Ampt Equation,
Lagrange's Inversion
Theorem,
Talsma-Parlange Equation,
Three-Parameter Infiltration
Equation

##### 344 Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model

**Authors:**
Hidetoshi Konno,
Akio Suzuki

**Abstract:**

The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.

**Keywords:**
Transient population dynamics,
Phase singularity,
Birth-death process,
Non-stationary Master equation,
nonlinear Langevin equation,
generalized Logistic equation.

##### 343 The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term

**Authors:**
Jaipong Kasemsuwan

**Abstract:**

**Keywords:**
Finite-difference method,
the nonlinear damped
equation,
the numerical simulation,
the suspended string equation

##### 342 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations

**Authors:**
Magdy G. Asaad

**Abstract:**

**Keywords:**
Bilinear operator,
G-BKP equation,
Integrable nonlinear PDEs,
Jimbo-Miwa equation,
Ma-Fan equation,
N-soliton solutions,
Pfaffian solutions.

##### 341 Numerical Study of Some Coupled PDEs by using Differential Transformation Method

**Authors:**
Reza Abazari,
Rasool Abazari

**Abstract:**

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

**Keywords:**
Coupled Korteweg-de Vries(KdV) equation,
Coupled Burgers equation,
Coupled Schrödinger equation,
differential transformation method.

##### 340 Modeling and Simulation of Acoustic Link Using Mackenize Propagation Speed Equation

**Authors:**
Christhu Raj M. R.,
Rajeev Sukumaran

**Abstract:**

**Keywords:**
Underwater Acoustics,
Mackenzie Speed Equation,
Temperature,
Salinity.

##### 339 Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations

**Authors:**
Ehsan Mahdavi

**Abstract:**

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

**Keywords:**
Exp-function method,
Rosenau Kawahara equation,
Rosenau Korteweg-de Vries equation,
nonlinear partial differential
equation.

##### 338 The Dividend Payments for General Claim Size Distributions under Interest Rate

**Authors:**
Li-Li Li,
Jinghai Feng,
Lixin Song

**Abstract:**

**Keywords:**
Dividend payout,
Integro-differential equation,
Jumpdiffusion model,
Volterra equation

##### 337 Analytical Solutions of Kortweg-de Vries(KdV) Equation

**Authors:**
Foad Saadi,
M. Jalali Azizpour,
S.A. Zahedi

**Abstract:**

**Keywords:**
Variational Iteration Method (VIM),
HomotopyPerturbation Method (HPM),
Homotopy Analysis Method (HAM),
KdV Equation.

##### 336 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

**Keywords:**
KdV equation,
Asymptotic Degeneracy,
Solitons,
Inverse Scattering

##### 335 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner.

##### 334 A FEM Study of Explosive Welding of Double Layer Tubes

**Authors:**
R. Alipour,
F.Najarian

**Abstract:**

**Keywords:**
Explosive Welding,
Johnson-Cook Equation,
Finite
Element,
JWL Equation.

##### 333 Mechanical Equation of State in an Al-Li Alloy

**Authors:**
Jung-Ho Moon,
Tae Kwon Ha

**Abstract:**

Existence of plastic equation of state has been investigated by performing a series of load relaxation tests at various temperatures using an Al-Li alloy. A plastic equation of state is first developed from a simple kinetics consideration for a mechanical activation process of a leading dislocation piled up against grain boundaries. A series of load relaxation test has been conducted at temperatures ranging from 200 to 530^{o}C to obtain the stress-strain rate curves. A plastic equation of state has been derived from a simple consideration of dislocation kinetics and confirmed by experimental results.

**Keywords:**
Plastic equation of state,
Dislocation kinetics,
Load relaxation test,
Al-Li alloy,
Microstructure.

##### 332 A Dynamic Equation for Downscaling Surface Air Temperature

**Authors:**
Ch. Surawut,
D. Sukawat

**Abstract:**

**Keywords:**
Dynamic Equation,
Downscaling,
Inverse distance
weight interpolation.

##### 331 Assessment of Hargreaves Equation for Estimating Monthly Reference Evapotranspiration in the South of Iran

**Authors:**
Ali Dehgan Moroozeh,
B. Farhadi Bansouleh

**Abstract:**

**Keywords:**
Evapotranspiration,
Hargreaves equation,
FAOPenman
method.

##### 330 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.

##### 329 Parallel Algorithm for Numerical Solution of Three-Dimensional Poisson Equation

**Authors:**
Alibek Issakhov

**Abstract:**

**Keywords:**
MPI,
OpenMP,
three dimensional Poisson equation

##### 328 Iterative solutions to the linear matrix equation AXB + CXTD = E

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
matrix equation,
iterative algorithm,
parameter estimation,
minimum norm solution.

##### 327 Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA

**Authors:**
G. Parmar,
R. Prasad,
S. Mukherjee

**Abstract:**

The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

**Keywords:**
Genetic algorithm,
Integral square error,
Orderreduction,
Stability equation method.