**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1451

# Search results for: generalized Pochhammer- Chree equation

##### 1451 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method

**Authors:**
Kourosh Parand,
Jamal Amani Rad

**Abstract:**

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

**Keywords:**
Exp-function method,
generalized Pochhammer- Chree equation,
solitary wave solution,
ODE's.

##### 1450 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.

##### 1449 Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation

**Authors:**
Kelong Zheng,
Jinsong Hu,

**Abstract:**

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

**Keywords:**
Generalized Rosenau-Burgers equation,
difference scheme,
stability,
convergence.

##### 1448 Lagrangian Method for Solving Unsteady Gas Equation

**Authors:**
Amir Taghavi,
kourosh Parand,
Hosein Fani

**Abstract:**

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

**Keywords:**
Unsteady gas equation,
Generalized Laguerre functions,
Lagrangian method,
Nonlinear ODE.

##### 1447 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability

**Authors:**
N. Kumaresan ,
J. Kavikumar,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
H-difference and Simulink.

##### 1446 Solving of the Fourth Order Differential Equations with the Neumann Problem

**Authors:**
Marziyeh Halimi,
Roushanak Lotfikar,
Simin Mansouri Borojeni

**Abstract:**

**Keywords:**
Neumann problem,
weighted Sobolev spaces,
generalized solution,
spectrum of linear operators.2000 mathematic subject classification: 34A05,
34A30.

##### 1445 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.

##### 1444 Note to the Global GMRES for Solving the Matrix Equation AXB = F

**Authors:**
Fatemeh Panjeh Ali Beik

**Abstract:**

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

**Keywords:**
Matrix equation,
Iterative method,
linear systems,
block Krylov subspace method,
global generalized minimum residual (Gl-GMRES).

##### 1443 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming

**Authors:**
N. Kumaresan,
J. Kavikumar,
M. Kumudthaa,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
Genetic programming and H-difference.

##### 1442 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 1441 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

**Authors:**
Aziz Sezgin

**Abstract:**

**Keywords:**
Backstepping,
boundary control,
2-D,
3-D,
n-D heat
equation,
distributed parameter systems.

##### 1440 Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F

**Authors:**
Fatemeh Panjeh Ali Beik

**Abstract:**

**Keywords:**
Matrix equations,
Iterative methods,
Block Krylovsubspace methods.

##### 1439 Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

**Authors:**
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
positive solution,
existence and uniqueness,
fixed point theorem,
generalized concave
and convex operator,
integral boundary conditions.

##### 1438 On Method of Fundamental Solution for Nondestructive Testing

**Abstract:**

**Keywords:**
ill-posed,
TSVD,
Laplace's equation,
inverse problem,
L-curve,
Generalized Cross Validation.

##### 1437 Adomian Method for Second-order Fuzzy Differential Equation

**Authors:**
Lei Wang,
Sizong Guo

**Abstract:**

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

**Keywords:**
Fuzzy-valued function,
fuzzy initial value problem,
strongly generalized differentiability,
adomian decomposition method.

##### 1436 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.

##### 1435 Influences of Thermal Relaxation Times on Generalized Thermoelastic Longitudinal Waves in Circular Cylinder

**Authors:**
Fatimah A. Alshaikh

**Abstract:**

This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.

**Keywords:**
Wave propagation,
longitudinal vibrations,
circular
cylinder,
generalized thermoelasticity,
Thermal relaxation times.

##### 1434 Generalized Fuzzy Subalgebras and Fuzzy Ideals of BCI-Algebras with Operators

**Authors:**
Yuli Hu,
Shaoquan Sun

**Abstract:**

**Keywords:**
BCI-algebras with operators,
generalized fuzzy subalgebras,
generalized fuzzy ideals,
generalized fuzzy quotient algebras.

##### 1433 A Comparison of Marginal and Joint Generalized Quasi-likelihood Estimating Equations Based On the Com-Poisson GLM: Application to Car Breakdowns Data

**Authors:**
N. Mamode Khan,
V. Jowaheer

**Abstract:**

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

**Keywords:**
Breakdowns,
under-dispersion,
com-poisson,
generalized linear model,
marginal quasi-likelihood estimation,
joint quasi-likelihood estimation.

##### 1432 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.

##### 1431 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 1430 The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

**Authors:**
Chao Yuan,
Bao Guang Tian

**Abstract:**

**Keywords:**
Generalized linear model,
generalized relative coefficient,
least eigenvalue,
relative efficiency.

##### 1429 Flutter Analysis of Slender Beams with Variable Cross Sections Based on Integral Equation Formulation

**Authors:**
Z. El Felsoufi,
L. Azrar

**Abstract:**

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

**Keywords:**
Chimney,
BEM and integral equation formulation,
non uniform cross section,
vibration and Flutter.

##### 1428 Generalized Chebyshev Collocation Method

**Authors:**
Junghan Kim,
Wonkyu Chung,
Sunyoung Bu,
Philsu Kim

**Abstract:**

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

**Keywords:**
Generalized Chebyshev Collocation method,
Generalized Chebyshev Polynomial,
Initial value problem.

##### 1427 The Gerber-Shiu Functions of a Risk Model with Two Classes of Claims and Random Income

**Authors:**
Shan Gao

**Abstract:**

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

**Keywords:**
Poisson process,
generalized Erlang risk process,
Gerber-Shiu function,
generating function,
generalized Lundberg equation.

##### 1426 The Particle Swarm Optimization Against the Runge’s Phenomenon: Application to the Generalized Integral Quadrature Method

**Authors:**
A. Zerarka,
A. Soukeur,
N. Khelil

**Abstract:**

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

**Keywords:**
Integral equation,
particle swarm optimization,
Runge's phenomenon.

##### 1425 (T1, T2)*- Semi Star Generalized Locally Closed Sets

**Authors:**
M. Sundararaman,
K. Chandrasekhara Rao

**Abstract:**

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

**Keywords:**
(T1,
T2)*-semi star generalized locally closed sets,
T1T2-semi star generalized closed sets.

##### 1424 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.

##### 1423 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

**Authors:**
Shazalina Mat Zin,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail,
Muhammad Abbas

**Abstract:**

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

**Keywords:**
Collocation method,
Cubic trigonometric B-spline,
Finite difference,
Wave equation.

##### 1422 New Application of EHTA for the Generalized(2+1)-Dimensional Nonlinear Evolution Equations

**Authors:**
Mohammad Taghi Darvishi,
Maliheh Najafi,
Mohammad Najafi

**Abstract:**

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

**Keywords:**
EHTA,
(2+1)-dimensional CBS equations,
(2+1)-dimensional breaking solution equation,
Hirota's bilinear form.