eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
1
13
3773
Monodromy problem for the degenerate critical points
Razie Shafeii Lashkarian
razie_sh@yahoo.com
1
Dariush Behmardi Sharifabad
behmardi@alzahra.ac.ir
2
Department of Mathematics, Alzahra University, Vanak, Tehran, Iran
Dariush Behmardi Sharifabad Department of Mathematics, Alzahra University, Vanak, Tehran, Iran
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
Monodromy problem
degenerate critical point
hyperbolic critical point
nilpotent critical point
blow up method
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
14
35
3798
Brenstien polynomials and its application to fractional differential equation
Hammad Khalil
hammadk310@gmail.com
1
Rahmat Khan
rahmat_alipk@yahoo.com
2
M. Rashidi
mm_rashidi@tongji.edu.cn
3
University of Malakand, KPK, Pakistan
Dean Faculty of Science, Departement of Mathematics, University of Malakand, KPK, Pakistan
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University. ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, China
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
Brenstien polynomials,Coupled system
Fractional differential equations
operational matrices of integrations
Numerical simulations
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
36
44
3799
Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients
Mahdiye Gholipour
m_gholipour@sut.ac.ir
1
Payam Mokhtary
mokhtary.payam@gmail.com
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
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
Discrete Galerkin method
Generalized Jacobi polynomials
Higher even-order Integro-Differential Equations
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
45
50
3800
A continuous approximation fitting to the discrete distributions using ODE
Hossein Bevrani
bevrani@gmail.com
1
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, 5166615648, Iran
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
Ordinary differential equations
Probability density functions
Pearson's family distribution
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
51
58
3885
A new family of four-step fifteenth-order root-finding methods with high efficiency index
Tahereh Eftekhari
t.eftekhari2009@gmail.com
1
Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan 987-98155, Iran
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
Nonlinear equations
Ostrowski's method
Order of convergence
Efficiency index
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2015-01-01
3
1
59
69
3886
Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation
Md. Nur Alam
nuralam.pstu23@gmail.com
1
Md. Mashiar Rahman
md.mashiur4182@gmail.com
2
Md. Rafiqul Islam
rafiqku.islam@gmail.com
3
Harun-Or- Roshid
harunorroshidmd@gmail.com
4
Department of Mathematics, Pabna University of Science and Technology, Bangladesh
Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Department of Mathematics, Pabna University of Science and Technology, Bangladesh
Department of Mathematics, Pabna University of Science and Technology, Bangladesh
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
New extended (G'/G)-expansion method
the Benjamin-Ono equation
exact solutions