2015
3
1
1
0
Monodromy problem for the degenerate critical points
2
2
For the polynomial planar vector fields with a hyperbolic or nilpotent critical point at the origin, the monodromy problem has been solved, but for the strongly degenerate critical points this problem is still open. When the critical point is monodromic, the stability problem or the center focus problem is an open problem too. In this paper we will consider the polynomial planar vector fields with a degenerate critical point at the origin. At first we give some normal form for the systems which has no characteristic directions. Then we consider the systems with some characteristic directions at which the origin is still a monodromic critical point and we give a monodromy criterion. Finally we clarify our work by some examples.
1

1
13


Razie
Shafeii Lashkarian
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Department of Mathematics,
Alzahra University,
Van
I. R. Iran
razie_sh@yahoo.com


Dariush
Behmardi Sharifabad
Dariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Dariush Behmardi Sharifabad
Department of
I. R. Iran
behmardi@alzahra.ac.ir
Monodromy problem
degenerate critical point
hyperbolic critical point
nilpotent critical point
blow up method
Brenstien polynomials and its application to fractional differential equation
2
2
The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is developed. The scheme is designed such a way that it can be easily simulated with any computational software. The efficiency of proposed method verified by some test problems.
1

14
35


Hammad
Khalil
University of Malakand, KPK, Pakistan
University of Malakand, KPK, Pakistan
Pakistan
hammadk310@gmail.com


Rahmat
Khan
Dean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, Pakistan
Dean Faculty of Science,
Departement of Mathematic
Pakistan
rahmat_alipk@yahoo.com


M.
Rashidi
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENNTongji Clean Energy Institute of advanced studies, Shanghai, China
Shanghai Key Lab of Vehicle Aerodynamics
China
mm_rashidi@tongji.edu.cn
Brenstien polynomials,Coupled system
Fractional differential equations
operational matrices of integrations
Numerical simulations
Discrete Galerkin Method for Higher EvenOrder IntegroDifferential Equations with Variable Coefficients
2
2
This paper presents discrete Galerkin method for obtaining the numerical solution of higher evenorder integrodifferential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiveness and wellposedness of the proposed method. In addition, the results obtained are compared with those obtained by well known Pseudospectral method, thereby confirming the superiority of our proposed scheme.
1

36
44


Mahdiye
Gholipour
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic
I. R. Iran
m_gholipour@sut.ac.ir


Payam
Mokhtary
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic
I. R. Iran
mokhtary.payam@gmail.com
Discrete Galerkin method
Generalized Jacobi polynomials
Higher evenorder IntegroDifferential Equations
A continuous approximation fitting to the discrete distributions using ODE
2
2
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential equations.
1

45
50


Hossein
Bevrani
Department of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, Iran
Department of Statistics,
Faculty of Mathematical
I. R. Iran
bevrani@gmail.com
Ordinary differential equations
Probability density functions
Pearson's family distribution
A new family of fourstep fifteenthorder rootfinding methods with high efficiency index
2
2
In this paper a new family of fifteenthorder methods with high efficiency index is presented. This family include four evaluations of the function and one evaluation of its first derivative per iteration. Therefore, this family of methods has the efficiency index which equals 1.71877. In order to show the applicability and validity of the class, some numerical examples are discussed.
1

51
58


Tahereh
Eftekhari
Faculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 98798155, Iran
Faculty of Mathematics,
University of Sistan
I. R. Iran
t.eftekhari2009@gmail.com
Nonlinear equations
Ostrowski's method
Order of convergence
Efficiency index
Application of the new extended (G'/G) expansion method to find exact solutions for nonlinear partial differential equation
2
2
In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the BenjaminOno equation. It is establish that the method by Roshid et al. is a very wellorganized method which can be used to find exact solutions of a large number of NLPDEs.
1

59
69


Md. Nur
Alam
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University
Bangladesh
nuralam.pstu23@gmail.com


Md.
Mashiar Rahman
Department of Mathematics,
Begum Rokeya University, Rangpur, Bangladesh
Department of Mathematics,
Begum Rokeya University
Bangladesh
md.mashiur4182@gmail.com


Md.
Rafiqul Islam
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University
Bangladesh
rafiqku.islam@gmail.com


HarunOr
Roshid
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University
Bangladesh
harunorroshidmd@gmail.com
New extended (G'/G)expansion method
the BenjaminOno equation
exact solutions