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