**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3246

# Search results for: Lane-Emden type equations

##### 3246 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.

##### 3245 Symmetries, Conservation Laws and Reduction of Wave and Gordon-type Equations on Riemannian Manifolds

**Authors:**
Sameerah Jamal,
Abdul Hamid Kara,
Ashfaque H. Bokhari

**Abstract:**

Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

**Keywords:**
Bianchi metric,
conservation laws,
Milne metric,
symmetries.

##### 3244 Very-high-Precision Normalized Eigenfunctions for a Class of Schrödinger Type Equations

**Authors:**
Amna Noreen ,
Kare Olaussen

**Abstract:**

We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

**Keywords:**
Eigenvalue problems,
bound states,
trapezoidal rule,
poisson resummation.

##### 3243 Ordinary Differential Equations with Inverted Functions

**Authors:**
Thomas Kampke

**Abstract:**

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

**Keywords:**
Euler method,
fixed points,
golden section,
multi-step procedures,
Runge Kutta methods.

##### 3242 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

**Authors:**
Oleksandr Poliakov,
Yevgen Pashkov,
Marina Kolesova,
Olena Chepenyuk,
Mykhaylo Kalinin,
Vadym Kramar

**Abstract:**

**Keywords:**
Iterative method,
Laguerre's method,
Newton's
method,
polynomial equation,
system of equations

##### 3241 Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials

**Authors:**
Gulgassyl Nugmanova,
Zhanat Zhunussova,
Kuralay Yesmakhanova,
Galya Mamyrbekova,
Ratbay Myrzakulov

**Abstract:**

**Keywords:**
Spin systems,
equivalent counterparts,
integrable
reductions,
self-consistent potentials.

##### 3240 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

**Authors:**
Fuziyah Ishak,
Siti Norazura Ahmad

**Abstract:**

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

**Keywords:**
Accuracy,
extended trapezoidal method,
numerical solution,
Volterra integro-differential equations.

##### 3239 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers

**Authors:**
Nurhakimah Ab. Rahman,
Lazim Abdullah

**Abstract:**

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

**Keywords:**
Dual fuzzy polynomial equations,
Interval type-2,
Ranking method,
Value.

##### 3238 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.

##### 3237 Numerical Solution of Hammerstein Integral Equations by Using Quasi-Interpolation

**Authors:**
M. Zarebnia,
S. Khani

**Abstract:**

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

**Keywords:**
Hammerstein integral equations,
quasi-interpolation,
Nystrom’s method.

##### 3236 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.

##### 3235 Solitary Wave Solutions for Burgers-Fisher type Equations with Variable Coefficients

**Authors:**
Amit Goyal,
Alka,
Rama Gupta,
C. Nagaraja Kumar

**Abstract:**

**Keywords:**
Solitary wave solution,
Variable coefficient Burgers-
Fisher equation,
Auxiliary equation method.

##### 3234 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.

##### 3233 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

**Authors:**
jianhua Hou,
Changqing Yang,
and Beibo Qin

**Abstract:**

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

**Keywords:**
Hybrid functions,
Fredholm integral equation,
Blockpulse,
Chebyshev polynomials,
product operational matrix.

##### 3232 Effect of Implementation of Nonlinear Sequence Transformations on Power Series Expansion for a Class of Non-Linear Abel Equations

**Authors:**
Javad Abdalkhani

**Abstract:**

**Keywords:**
Nonlinear transformation,
Abel Volterra Equations,
Mathematica

##### 3231 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.

##### 3230 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method

**Authors:**
Changqing Yang,
Jianhua Hou

**Abstract:**

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

**Keywords:**
Integro-differential equations,
Laplace transform,
fractional derivative,
adomian polynomials,
pade appoximants.

##### 3229 Dynamic Analysis of a Moderately Thick Plate on Pasternak Type Foundation under Impact and Moving Loads

**Authors:**
Neslihan Genckal,
Reha Gursoy,
Vedat Z. Dogan

**Abstract:**

In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

**Keywords:**
Elastic foundation,
impact,
moving load,
thick plate.

##### 3228 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

##### 3227 1-D Modeling of Hydrate Decomposition in Porous Media

**Authors:**
F. Esmaeilzadeh,
M. E. Zeighami,
J. Fathi

**Abstract:**

This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.

**Keywords:**
Hydrate reservoir,
numerical modeling,
depressurization,
thermal stimulation,
gas generation.

##### 3226 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

##### 3225 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.

##### 3224 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.

##### 3223 A First Course in Numerical Methods with “Mathematica“

**Authors:**
Andrei A. Kolyshkin

**Abstract:**

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

##### 3222 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.

##### 3221 Numerical Modeling of Wave Run-Up in Shallow Water Flows Using Moving Wet/Dry Interfaces

**Authors:**
Alia Alghosoun,
Michael Herty,
Mohammed Seaid

**Abstract:**

**Keywords:**
Run-up waves,
Shallow water equations,
finite volume
method,
wet/dry interface,
dam-break problem.

##### 3220 The Pell Equation x2 − (k2 − k)y2 = 2t

**Authors:**
Ahmet Tekcan

**Abstract:**

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

##### 3219 Sixth-Order Two-Point Efficient Family of Super-Halley Type Methods

**Authors:**
Ramandeep Behl,
S. S. Motsa

**Abstract:**

**Keywords:**
Basins of attraction,
nonlinear equations,
simple roots,
Super-Halley.

##### 3218 The Euler Equations of Steady Flow in Terms of New Dependent and Independent Variables

**Authors:**
Peiangpob Monnuanprang

**Abstract:**

In this paper we study the transformation of Euler equations 1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

**Keywords:**
Euler equations,
transformation,
hyperbolic,
elliptic

##### 3217 Theoretical Study on the Forced Vibration of One Degree of Freedom System, Equipped with Inerter, under Load-Type or Displacement-Type Excitation

**Authors:**
Barenten Suciu

**Abstract:**

In this paper, a theoretical study on the forced vibration of one degree of freedom system equipped with inerter, working under load-type or displacement-type excitation, is presented. Differential equations of movement are solved under cosinusoidal excitation, and explicit relations for the magnitude, resonant magnitude, phase angle, resonant frequency, and critical frequency are obtained. Influence of the inertance and damping on these dynamic characteristics is clarified. From the obtained results, one concludes that the inerter increases the magnitude of vibration and the phase angle of the damped mechanical system. Moreover, the magnitude ratio and difference of phase angles are not depending on the actual type of excitation. Consequently, such kind of similitude allows for the comparison of various theoretical and experimental results, which can be broadly found in the literature.

**Keywords:**
One degree of freedom vibration,
inerter,
parallel connection,
load-type excitation,
displacement-type excitation.