University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
Monodromy problem for the degenerate critical points
1
13
EN
Razie
Shafeii Lashkarian
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
razie_sh@yahoo.com
Dariush
Behmardi Sharifabad
Dariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, Iran
behmardi@alzahra.ac.ir
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.
Monodromy problem,degenerate critical point,hyperbolic critical point,nilpotent critical point,blow up method
http://cmde.tabrizu.ac.ir/article_3773.html
http://cmde.tabrizu.ac.ir/article_3773_abd632cbb0a50fae55f87a7fd04abd3b.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
Brenstien polynomials and its application to fractional differential equation
14
35
EN
Hammad
Khalil
University of Malakand, KPK, Pakistan
hammadk310@gmail.com
Rahmat
Khan
Dean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, Pakistan
rahmat_alipk@yahoo.com
M.
Rashidi
Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, China
mm_rashidi@tongji.edu.cn
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.
Brenstien polynomials,Coupled system,Fractional differential equations,operational matrices of integrations,Numerical simulations
http://cmde.tabrizu.ac.ir/article_3798.html
http://cmde.tabrizu.ac.ir/article_3798_54b86cd79ac7d1a5e159da4320fe9f5a.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients
36
44
EN
Mahdiye
Gholipour
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
m_gholipour@sut.ac.ir
Payam
Mokhtary
Department of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, Iran
mokhtary.payam@gmail.com
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.
Discrete Galerkin method,Generalized Jacobi polynomials,Higher even-order Integro-Differential Equations
http://cmde.tabrizu.ac.ir/article_3799.html
http://cmde.tabrizu.ac.ir/article_3799_b43e56719f7a409023def050c681084e.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
A continuous approximation fitting to the discrete distributions using ODE
45
50
EN
Hossein
Bevrani
Department of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, Iran
bevrani@gmail.com
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.
Ordinary differential equations,Probability density functions,Pearson's family distribution
http://cmde.tabrizu.ac.ir/article_3800.html
http://cmde.tabrizu.ac.ir/article_3800_f745eda5291740921262040f296adf0c.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
A new family of four-step fifteenth-order root-finding methods with high efficiency index
51
58
EN
Tahereh
Eftekhari
Faculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 987-98155, Iran
t.eftekhari2009@gmail.com
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.
Nonlinear equations,Ostrowski's method,Order of convergence,Efficiency index
http://cmde.tabrizu.ac.ir/article_3885.html
http://cmde.tabrizu.ac.ir/article_3885_c17d30902b762fd0dc8d52a6e041e419.pdf
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
3
1
2015
01
01
Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation
59
69
EN
Md. Nur
Alam
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
nuralam.pstu23@gmail.com
Md.
Mashiar Rahman
Department of Mathematics,
Begum Rokeya University, Rangpur, Bangladesh
md.mashiur4182@gmail.com
Md.
Rafiqul Islam
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
rafiqku.islam@gmail.com
Harun-Or-
Roshid
Department of Mathematics,
Pabna University of Science and Technology, Bangladesh
harunorroshidmd@gmail.com
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.
New extended (G'/G)-expansion method,the Benjamin-Ono equation,exact solutions
http://cmde.tabrizu.ac.ir/article_3886.html
http://cmde.tabrizu.ac.ir/article_3886_2bd1c0b9a5f11541d167f7414573fda6.pdf