2017
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New analytical soliton type solutions for double layers structure model of extended KdV equation
2
2
In this present study the double layers structure model of extended Kortewegde Vries(KdV) equation will be obtained with the help of the reductive perturbation method, which admits a double layer structure in current plasma model. Then by using of new analytical method we obtain the new exact solitary wave solutions of this equation. Double layer is a structure in plasma and consists of two parallel layers with opposite electrical charge.The sheets of charge cause a strong electric field and a correspondingly sharp change in electrical potential across the double layer. As a result, they are expected to be an important process in many different types of space plasmas on Earth and on many astrophysical objects. These nonlinear structures can occur naturally in a variety of space plasmas environment. They are described by the Kortewegde Vries(KdV) equation with additional term of cubic nonlinearity in different homogeneous plasma systems. The performance of this method is reliable, simple and gives many new exact solutions. The (G'/G)expansion method has more advantages: It is direct and concise.
1

256
270


Ahmad
Neirameh
Department of Mathematics, Faculty of sciences, Gonbad Kavous University, Gonbad, Iran
Department of Mathematics, Faculty of sciences,
I. R. Iran
a.neirameh@gmail.com


Nafiseh
Memarian
Faculty of Physics, Semnan University, Semnan, Iran
Faculty of Physics, Semnan University, Semnan,
I. R. Iran
n.memarian@semnan.ac.ir
Double layers
Extended Kortewegde Vries(KdV)
Analytical method
Invariant functions for solving multiplicative discrete and continuous ordinary differential equations
2
2
In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference equations and differential equations are investigated and solved by making use multiplicative difference and differential equations
1

271
279


Reza
Hosseini Komlaei
Department of Mathematics, Azarbaijan Shahid Madani University,
35 Km TabrizMaraghe Road, Tabriz, Iran
Department of Mathematics, Azarbaijan Shahid
I. R. Iran
hosseinik@azaruniv.edu


Mohammad
Jahanshahi
Department of Mathematics, Azarbaijan Shahid Madani University,
35 Km TabrizMaraghe Road, Tabriz, Iran
Department of Mathematics, Azarbaijan Shahid
I. R. Iran
jahanshahi@azaruniv.edu
Multiplicative Continuous calculus
Invariant Functions
Multiplicative Discrete calculus
A numerical study of electrohydrodynamic flow analysis in a circular cylindrical conduit using orthonormal Bernstein polynomials
2
2
In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an iondrag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized to narrow down the computation of nonlinear boundary value problem to the solution of algebraic equations. Also, by using the residual correction process, an efficient error estimation is introduced. Graphical and tabular results are presented to investigate the influence of the strength of nonlinearity $alpha$ and Hartmann electric number $Ha^2$ on velocity profiles. The significant merit of this method is that it can yield an appropriate level of accuracy even with large values of $alpha$ and $Ha^2$. Compared with recent works, the numerical experiments in this study show a good agreement with the results obtained by using MATLAB solver bvp5c and its competitive ability.
1

280
300


Ehsan
Hosseini
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
I. R. Iran
ehosseini@stu.yazd.ac.ir


Ghasem
Barid Loghmani
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
I. R. Iran
loghmani@yazd.ac.ir


Mohammad
Heydari
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University,
I. R. Iran
m.heydari@yazd.ac.ir


AbdulMajid
Wazwaz
Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA
Department of Mathematics, Saint Xavier University
Iran
wazwaz@sxu.edu
Electrohydrodynamics flow
Circular cylindrical conduit
Hartmann electric number
Orthonormal Bernstein polynomials
An approximation to the solution of BenjaminBonaMahonyBurgers equation
2
2
In this paper, numerical solution of the BenjaminBonaMahonyBurgers (BBMB) equation is obtained by using the meshfree method based on the collocation method with radial basis functions (RBFs). Stability analysis of the method is discussed. The method is applied to several examples and accuracy of the method is tested in terms of $L_2$ and $L_infty$ error norms.
1

301
309


Mohammad
Zarebnia
Department of Mathematics and Applications, University of Mohaghegh Ardabili, 5619911376, Ardabil, Iran
Department of Mathematics and Applications,
I. R. Iran
zarebnia@uma.ac.ir


Maryam
Aghili
Department of Mathematics and Applications, University of Mohaghegh Ardabili, 5619911376, Ardabil, Iran
Department of Mathematics and Applications,
I. R. Iran
mina.aghili66@yahoo.com
Radial basis functions
Meshfree method
BBMB equation
Stability
Existence results of infinitely many solutions for a class of p(x)biharmonic problems
2
2
The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.
1

310
323


Saeid
Shokooh
Department of Mathematics, Faculty of Sciences,
Gonbad Kavous University, Gonbad Kavous, Iran
Department of Mathematics, Faculty of Sciences,
Go
I. R. Iran
shokooh@gonbad.ac.ir


Ghasem
Alizadeh Afrouzi
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical
I. R. Iran
afrouzi@umz.ac.ir
Ricceri's Variational Principle
infinitely many solutions
Navier condition
$p(x)$biharmonic type operators
On second derivative 3stage HermiteBirkhoffObrechkoff methods for stiff ODEs: Astable up to order 10 with variable stepsize
2
2
Variablestep (VS) second derivative $k$step $3$stage HermiteBirkhoffObrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$step methods of order $(p2)$ and a second derivative twostep diagonally implicit $3$stage HermiteBirkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for considering this class of formulae is to obtain a set of $k$step methods which are $L$stable and are suitable for the integration of stiff differential systems whose Jacobians have some large eigenvalues lying close to the imaginary axis with negative real part. The approach, described in the present paper, allows us to develop $L$stable $k$step methods of order up to 10. Selected HBO($p$) of order $p$, $p=9,10$, compare favorably with existing Cash $L$stable second derivative extended backward differentiation formulae, SDEBDF($p$), $p=7,8$ in solving problems often used to test stiff ODE solvers.
1

324
347


Truong
NguyenBa
Department of Mathematics and Statistics,
University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Department of Mathematics and Statistics,
Universi
Canada
trnguyen@uottawa.ca


Thierry
Giordano
Department of Mathematics and Statistics,
University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Department of Mathematics and Statistics,
Universi
Canada
giordano@uottawa.ca


Remi
Vaillancourt
Department of Mathematics and Statistics,
University of Ottawa, Ottawa, Ontario, Canada K1N 6N5
Department of Mathematics and Statistics,
Universi
Canada
remi@uottawa.ca
HermiteBirkhoff methods
generalized DIRK methods
$A$stable
oscillatory stiff DETEST problems
confluent Vandermondetype systems