Prof. Mohammed salah El Din El Sayed

Paper (1)

Space-charge-limited current, trap distribution and optical energy gap in

amorphous (In13Se87 and In20Se80) thin films

S.M. El-Sayed

Abstract

This paper shows that In13Se87 and In20Se80 thin films can be prepared by thermal

evaporation technique. Current density–voltage (J–V) characteristics and thermally

stimulated currents have been obtained. Coplanar silver electrodes were used. At low

voltages, the current density behavior suggests ohmic conductivity, while at higher

voltages, a region of space-charge-limited current conduction was observed. The analysis

of the temperature dependence of J–V curves yields the following parameters: barrier

height ϕb, energy of activation trap Et, trapping factor θ, trap density Nt, and

concentration of the free carriers, n0. The transition from ohmic to square law behavior

was used to calculate all of these parameters. It was found that by increasing the In at%

the trap density increased from 1.62×1015 to 3.12×1017 cm−3 and the trap activation

energy Et, increases from 0.062 to 0.087 eV.

The optical absorption of these films was studied in the UV-VIS spectral range and the

value of the optical energy gap was determined. The results of changes in the J–V

characteristics and optical energy gap are discussed using a simple consideration, based

on average coordination numbers, cohesive energy and bond energies.

Keywords:

( Chalcogenide glasses; Current density–voltage; Space-charge; Barrier height)

Cited by (21)

Paper (2)

Iterative methods for the extremal positive definite solution of the matrix

equation X+A*X-αA=Q

Zhen-yun Penga, Salah M. El-Sayedb, Xiang-lin Zhanga

Abstract:

In this paper, the inversion free variant of the basic fixed point iteration methods for

obtaining the maximal positive definite solution of the nonlinear matrix equation X+A*X-

αA=Q with the case 0<α⩽1 and the minimal positive definite solution of the same matrix

equation with the case α⩾1 are proposed. Some necessary conditions and sufficient

conditions for the existence of positive definite solutions for the matrix equation are

derived. Numerical examples to illustrate the behavior of the considered algorithms are

also given.

Keywords

Positive definite matrix; Matrix equation; Iterative method; The maximal solution;

The minimal solution.

Paper (3)

A comparison of Adomian's decomposition method and wavelet-Galerkin

method for solving integro-differential equations

Salah M. El-Sayed a. Mohammedi R. Abdel-Azizb

Abstract

This paper aims to introduce a comparison of Adomian decomposition method and

wavelet-Galerkin method for the solution of integro-differential equations. From the

computational viewpoint, the comparison shows that the Adomian decomposition method

is efficient and easy to use.

Keywords

Adomian decomposition method; Wavelet-Galerkin method; Integro-differential

equations

Cited by (37)

Paper (4)

A new modification of the Adomian decomposition method for linear and

nonlinear operators

Abdul-Majid Wazwaza Salah M. El-Sayedb

Abstract

In this paper we present an efficient modification of the Adomian decomposition method

that will facilitate the calculations. We then conduct a comparative study between the

new modification and the modified decomposition method. The study is conducted

through illustrative examples. The new modification introduces a promising tool for

many linear and nonlinear models.

Keywords

( Linear and nonlinear operators; Adomian decomposition method; Adomian polynomials)

Cited by (150)

Paper (5)

A numerical simulation and explicit solutions of the generalized Burgers–

Fisher equation

Doǧan Kayaa Salah M. El-Sayed

Abstract

We consider solitary-wave solutions of the generalized Burgers–Fisher (BF) equation

ut+purux−uxx−qu(1−u

r)=0. In this paper by considering the decomposition scheme, we

first obtain the exact solutions of the generalized BF equation for the initial condition

without using any classical transformations and then its numerical solutions are

constructed without using any discretization technique. The numerical solutions are

compared with the known analytical solutions. Its remarkable accuracy is finally

demonstrated in the study of some values r⩾2 of the generalized BF equation.

Keywords

( The decomposition method; Generalized Burgers–Fisher equation; Solitary-

wave solution; Numerical results)

Cited by (29)

Paper (6)

A numerical solution and an exact explicit solution of the NLS equation

Salah M. El-Sayeda Dogˇan Kayab

Abstract

We consider traveling wave solutions of the nonlinear Schrödinger (NLS for short)

equation. In this paper by considering the decomposition scheme, we first obtain the

exact solutions of the NLS equation for the initial condition without using any classical

transformations and then its numerical solutions are constructed without using any

discretization technique. The numerical solutions are compared with the known analytical

solutions. Its remarkable accuracy is finally demonstrated in the study of some initial

values of the NLS equation.

Keywords

(The decomposition method; Nonlinear Schrödinger equation; traveling wave

solutions; Numerical results)

Cited by (22)

Paper (7)

A numerical solution of the Klein–Gordon equation and convergence of

the decomposition method

Doǧan Kayaa, Salah M. El-Sayed

Abstract

The decomposition method for solving the Klein–Gordon equation has been

implemented. The explicit and numerical solutions of the equation are calculated in the

form of convergent power series with easily computable components. The present

method performs extremely well in terms of accuracy, efficiency, simplicity, stability and

reliability. We also proved the convergence of Adomian's decomposition method for the

nonlinear Klein–Gordon equation.

Keywords

( Decomposition method; Modified decomposition method; Convergence of the decomposition

method; Nonlinear Klein–Gordon equations)

Cited by ( 28)

Paper (8)

An application of the ADM to seven-order Sawada–Kotara equations

Salah M. El-Sayeda Doǧan Kayab

Abstract

We implemented the Adomian decomposition method (for short, ADM) for

approximating the solution of the seventh-order Sawada–Kotera (for short, sSK) and a

Lax's seventh-order KdV (for short, LsKdV) equations. By using this scheme, explicit

exact solution is calculated. We obtain the exact solitary-wave solutions and numerical

solutions of the LsKdV and sSK equations for the initial conditions. The numerical

solutions are compared with the known analytical solutions. Their remarkable accuracy

are finally demonstrated for the both seven-order equations.

Keywords

The Adomian decomposition method; The seventh-order Sawada–Kotera equation; Lax's

seventh-order KdV equation; Solitary-wave solution; The convergence of Adomian

decomposition method

Cited by (41)

Paper (9)

An application of the decomposition method for the generalized KdV and

RLW equations

Doǧan Kayaa Salah M. El-Sayed

Abstract

We consider solitary-wave solutions of the generalized regularized long-wave (RLW)

and Korteweg-de Vries (KdV) equations. We prove the convergence of Adomian

decomposition method applied to the generalized RLW and KdV equations. Then we

obtain the exact solitary-wave solutions and numerical solutions of the generalized RLW

and KdV equations for the initial conditions. The numerical solutions are compared with

the known analytical solutions. Their remarkable accuracy are finally demonstrated for

the generalized RLW and KdV equations.

Cited by (103)

Paper (10)

Comparing numerical methods for Helmholtz equation model problem

Salah M. El-Sayed Doǧan Kayab

Abstract

In this article, we implement a relatively new numerical technique, Adomian’s

decomposition method for solving the linear Helmholtz partial differential equations. The

method in applied mathematics can be an effective procedure to obtain for the analytic

and approximate solutions. A new approach to a linear or nonlinear problems is

particularly valuable as a tool for Scientists and Applied Mathematicians, because it

provides immediate and visible symbolic terms of analytic solution as well as its

numerical approximate solution to both linear and nonlinear problems without

linearization [Solving Frontier Problems of Physics: The Decomposition Method, Kluwer

Academic Publishers, Boston, 1994; J. Math. Anal. Appl. 35 (1988) 501]. It does also not

require discretization and consequently massive computation. In this scheme the solution

is performed in the form of a convergent power series with easily computable

components. This paper will present a numerical comparison with the Adomian

decomposition and a conventional finite-difference method. The numerical results

demonstrate that the new method is quite accurate and readily implemented.

Keywords:

The Adomian decomposition method; Finite-difference method; The Helmholtz equation model

problem

Cited by (26)

Paper (11)

Effect of electron beam irradiation on the conduction phenomena of

unplasticized PVC/PVA copolymer

S.M. El-Sayed H.M. Abdel Hamid R.M. Radwan

Abstract

The effect of electron beam irradiation on the conduction phenomenon of unplasticized

PVC/PVA copolymer has been investigated. The current–voltage (J–V) characteristics in

the voltage range 0.1–60 V were measured for films irradiated with different doses; 150,

550 and 1100 kGy. The temperature dependence of the J–V characteristics in the

temperature range 303–343 K was obtained. The results indicated that the conduction as a

function of the applied voltage depends on the presence of localized state or the trapping

levels positioned at a specific energy Et below the conduction band. Therefore, the charge

carrier's concentration in the conduction band, trapping parameter θ, electron mobility μ0,

effective electron drift mobility μe as well as Fermi level energy Ef and trapping energy Et

were estimated as a function of dose.

Keywords

UPVC/PVA copolymer; Electron beam irradiation; (J–V) characteristics; Electrical conduction

parameters

Cited by (39)

Paper (12)

Higher order pseudospectral differentiation matrices

Elsayed M.E. Elbarbarya Salah M. El-Sayed

Abstract

A new explicit expression of the higher order pseudospectral differentiation matrices is

presented by using an explicit formula for higher derivatives of Chebyshev polynomials.

The roundoff errors incurred during computing differentiation matrices are investigated.

The advantages of the suggested differentiation matrices emerged through comparisons

with other ones.

Keywords

( Chebyshev collocation; Differentiation matrix; Roundoff error; Chebyshev polynomials )

Cited by (23)

Paper (13)

Numerical soliton-like solutions of the potential Kadomtsev–Petviashvili

equation by the decomposition method

Doǧan Kayaa Salah M. El-Sayed

Abstract:

In this Letter we present an Adomian's decomposition method (shortly ADM) for

obtaining the numerical soliton-like solutions of the potential Kadomtsev–Petviashvili

(shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact

and numerical solitary-wave solutions of the PKP equation for certain initial conditions.

Then ADM yields the analytic approximate solution with fast convergence rate and high

accuracy through previous works. The numerical solutions are compared with the known

analytical solutions.

Keywords:

(2+1)-dimensional potential Kadomtsev–Petviashvili equation; Soliton-like solutions; Adomian

decomposition method

Cited by (43)

Paper (14)

On a generalized fifth order KdV equations

Doǧan Kayaa Salah M. El-Sayed

Abstract

In this Letter, we dealt with finding the solutions of a generalized fifth order KdV

equation (for short, gfKdV) by using the Adomian decomposition method (for short,

ADM). We prove the convergence of ADM applied to the gfKdV equation. Then we

obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation

for the initial conditions. The numerical solutions are compared with the known

analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV

equation.

Keywords

Adomian decomposition method; Sawada–Kotera equation; Lax's fifth order KdV

equation; Solitary-wave solution; Convergence of Adomian decomposition method

Cited by (55)

Paper (15)

On an Iteration Method for Solving a Class of Nonlinear Matrix

Equations

Salah M. El-Sayed André C. M. Ran

Abstract

This paper treats a set of equationsof the form $X+A^{\star}{\cal F}(X)A =Q$, where

${\cal F}$ maps positive definite matrices either into positive definite matrices or into

negative definite matrices, and satisfies some monotonicity property. Here A is arbitrary

and Q is a positive definite matrix. It is shown that under some conditions an iteration

method converges to a positive definite solution. An estimate for the rate of convergence

is given under additional conditions, and some numerical results are given. Special cases

are considered, which cover also particular cases of the discrete algebraic Riccati

equation.

Keywords

matrix equation, iteration methods, operator monotone functions, hermitian positive

definite matrices

Paper (16)

On the numerical solution of the system of two-dimensional Burgers'

equations by the decomposition method

Salah M. El-Sayeda, Doǧan Kayab

Abstract

Adomian's decomposition method (ADM) is proposed to approximate the numerical and

analytical solutions of system two-dimensional Burgers' equations (STDBE) with initial

conditions. The advantages of this work are the decomposition method reduces the

computational work and improvement with regard to its accuracy and rapid convergence.

Some examples are given to illustrate the performance of the method described.

Keywords

Two-dimensional Burgers' equations; Adomian's decomposition method; Adomian's

polynomials

Cited by (28)

Paper (17)

On the solution of the coupled Schrödinger–KdV equation by the

decomposition method

Doǧan Kayaa Salah M. El-Sayed

Abstract

In this Letter, we consider a coupled Schrödinger–Korteweg–de Vries equation (or Sch–

KdV) equation with appropriate initial values using the Adomian's decomposition

method (or ADM). In this method, the solution is calculated in the form of a convergent

power series with easily computable components. The method does not need

linearization, weak nonlinearity assumptions or perturbation theory. The convergence of

the method as applied to Sch–KdV is illustrated numerically.

Keywords

Adomian decomposition method; Coupled Schrödinger–KdV equation; Traveling wave solution;

Numerical solution

Cited by (43)

Paper (18)

Properties of positive definite solutions of the equation X + A∗ X−2A = I

Ivan G. Ivanovb Salah M. El-sayed

Abstract

In this paper we discuss some properties of a positive definite solution of the matrix

equation X + A∗X−2 A = I. Two effective iterative methods for computing a positive

definite solution of this equation are proposed. Necessary and sufficient conditions for

existence of a positive definite solution are derived. Numerical experiments are executed

with these methods.

Keywords

Matrix equation; Positive definite solution; Iterative method

Cited by (68)

Paper (19)

The decomposition method for solving (2 + 1)-dimensional Boussinesq

equation and (3 + 1)-dimensional KP equation

Salah M. El-Sayed Doǧan Kayab

Abstract

We study the solitary-wave solutions of the (2 + 1)-dimensional Boussinesq equation

utt−uxx−uyy−(u2)xx−uxxxx=0 and (3 + 1)-dimensional KP equation

uxt−6ux2+6uuxx−uxxxx−uyy−uzz=0. In this paper by considering the decomposition scheme,

we first obtain the exact solitary-wave solutions of the (2 + 1)-dimensional Boussinesq

equation and (3 + 1)-dimensional KP equation for the initial conditions without using any

classical transformations and then its numerical solutions are constructed without using

any discretization technique. The numerical solutions are compared with the known

analytical solutions. Its remarkable accuracy is finally demonstrated in the study of

(2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation.

Keywords

(2 + 1)-dimensional Boussinesq equation; (3 + 1)-dimensional KP equation; Solitary-

wave solutions; Numerical solutions; Decomposition method

Cited by 23

Paper (20)

The decomposition method for studying the Klein–Gordon equation

Salah M El-Sayed

Abstract

In this paper we use Adomian’s decomposition method for solving linear and nonlinear

Klein–Gordon and sine-Gordon equations. Analytic and numerical studies are presented.

The obtained results show improvements over existing techniques.

Cited by 54

Paper (21)

The modified decomposition method for solving nonlinear algebraic

equations

Salah M. El-Sayed

Abstract

In this paper an algorithm based on Adomian's decomposition method is developed to

approximate the solution of nonlinear algebraic equations. The conditions of the

convergence which depend on the coefficients of the equation are found. The truncation

error of the method is obtained. Special cases of the nonlinear algebraic equation are

solved using the modified algorithm. The presented work shows that the modified

approach gives improvements over existing techniques.

Keywords

Nonlinear algebraic equations; Adomian's decomposition method; Adomian polynomials

Cited by 20