ORIGINAL_ARTICLE
Monodromy problem for the degenerate critical points
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.
http://cmde.tabrizu.ac.ir/article_3773_abd632cbb0a50fae55f87a7fd04abd3b.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
1
13
Monodromy problem
degenerate critical point
hyperbolic critical point
nilpotent critical point
blow up method
Razie
Shafeii Lashkarian
razie_sh@yahoo.com
true
1
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
LEAD_AUTHOR
Dariush
Behmardi Sharifabad
behmardi@alzahra.ac.ir
true
2
Dariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Dariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
Dariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
AUTHOR
ORIGINAL_ARTICLE
Brenstien polynomials and its application to fractional differential equation
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.
http://cmde.tabrizu.ac.ir/article_3798_54b86cd79ac7d1a5e159da4320fe9f5a.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
14
35
Brenstien polynomials,Coupled system
Fractional differential equations
operational matrices of integrations
Numerical simulations
Hammad
Khalil
hammadk310@gmail.com
true
1
University of Malakand, KPK, Pakistan
University of Malakand, KPK, Pakistan
University of Malakand, KPK, Pakistan
LEAD_AUTHOR
Rahmat
Khan
rahmat_alipk@yahoo.com
true
2
Dean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, Pakistan
Dean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, Pakistan
Dean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, Pakistan
AUTHOR
M.
Rashidi
mm_rashidi@tongji.edu.cn
true
3
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, China
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, China
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, China
AUTHOR
ORIGINAL_ARTICLE
Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients
This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential 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.
http://cmde.tabrizu.ac.ir/article_3799_b43e56719f7a409023def050c681084e.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
36
44
Discrete Galerkin method
Generalized Jacobi polynomials
Higher even-order Integro-Differential Equations
Mahdiye
Gholipour
m_gholipour@sut.ac.ir
true
1
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
AUTHOR
Payam
Mokhtary
mokhtary.payam@gmail.com
true
2
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
A continuous approximation fitting to the discrete distributions using ODE
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.
http://cmde.tabrizu.ac.ir/article_3800_f745eda5291740921262040f296adf0c.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
45
50
Ordinary differential equations
Probability density functions
Pearson's family distribution
Hossein
Bevrani
bevrani@gmail.com
true
1
Department of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, Iran
Department of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, Iran
Department of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
A new family of four-step fifteenth-order root-finding methods with high efficiency index
In this paper a new family of fifteenth-order 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.
http://cmde.tabrizu.ac.ir/article_3885_c17d30902b762fd0dc8d52a6e041e419.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
51
58
Nonlinear equations
Ostrowski's method
Order of convergence
Efficiency index
Tahereh
Eftekhari
t.eftekhari2009@gmail.com
true
1
Faculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 987-98155, Iran
Faculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 987-98155, Iran
Faculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 987-98155, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation
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 Benjamin-Ono equation. It is establish that the method by Roshid et al. is a very well-organized method which can be used to find exact solutions of a large number of NLPDEs.
http://cmde.tabrizu.ac.ir/article_3886_2bd1c0b9a5f11541d167f7414573fda6.pdf
2015-01-01T11:23:20
2018-11-13T11:23:20
59
69
New extended (G'/G)-expansion method
the Benjamin-Ono equation
exact solutions
Md. Nur
Alam
nuralam.pstu23@gmail.com
true
1
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
LEAD_AUTHOR
Md.
Mashiar Rahman
md.mashiur4182@gmail.com
true
2
Department of Mathematics,
Begum Rokeya University, Rangpur, Bangladesh
Department of Mathematics,
Begum Rokeya University, Rangpur, Bangladesh
Department of Mathematics,
Begum Rokeya University, Rangpur, Bangladesh
AUTHOR
Md.
Rafiqul Islam
rafiqku.islam@gmail.com
true
3
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
AUTHOR
Harun-Or-
Roshid
harunorroshidmd@gmail.com
true
4
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
AUTHOR