University of TabrizComputational Methods for Differential Equations2345-39823120150101Monodromy problem for the degenerate critical points1133773ENRazieShafeii LashkarianDepartment of Mathematics,
Alzahra University,
Vanak, Tehran, IranDariushBehmardi SharifabadDariush Behmardi Sharifabad
Department of Mathematics,
Alzahra University,
Vanak, Tehran, IranJournal Article20150408For 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.https://cmde.tabrizu.ac.ir/article_3773_abd632cbb0a50fae55f87a7fd04abd3b.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823120150101Brenstien polynomials and its application to fractional differential equation14353798ENHammadKhalilUniversity of Malakand, KPK, PakistanRahmatKhanDean Faculty of Science,
Departement of Mathematics,
University of Malakand, KPK, PakistanM.RashidiShanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University.
ENN-Tongji Clean Energy Institute of advanced studies, Shanghai, ChinaJournal Article20150126The 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.https://cmde.tabrizu.ac.ir/article_3798_54b86cd79ac7d1a5e159da4320fe9f5a.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823120150101Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients36443799ENMahdiyeGholipourDepartment of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, IranPayamMokhtaryDepartment of Mathematics,
Faculty of Basic Sciences,
Sahand University of Technology, Tabriz, IranJournal Article20150618This 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.https://cmde.tabrizu.ac.ir/article_3799_b43e56719f7a409023def050c681084e.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823120150101A continuous approximation fitting to the discrete distributions using ODE45503800ENHosseinBevraniDepartment of Statistics,
Faculty of Mathematical Sciences,
University of Tabriz, Tabriz, 5166615648, IranJournal Article20150817The 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.https://cmde.tabrizu.ac.ir/article_3800_f745eda5291740921262040f296adf0c.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823120150101A new family of four-step fifteenth-order root-finding methods with high efficiency index51583885ENTaherehEftekhariFaculty of Mathematics,
University of Sistan and Baluchestan,
Zahedan 987-98155, Iran0000-0002-4321-4450Journal Article20150201In 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.https://cmde.tabrizu.ac.ir/article_3885_c17d30902b762fd0dc8d52a6e041e419.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823120150101Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation59693886ENMd. NurAlamDepartment of Mathematics,
Pabna University of Science and Technology, Bangladesh0000-0001-6815-678XMd.Mashiar RahmanDepartment of Mathematics,
Begum Rokeya University, Rangpur, BangladeshMd.Rafiqul IslamDepartment of Mathematics,
Pabna University of Science and Technology, BangladeshHarun-Or-RoshidDepartment of Mathematics,
Pabna University of Science and Technology, BangladeshJournal Article20150112In 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.https://cmde.tabrizu.ac.ir/article_3886_2bd1c0b9a5f11541d167f7414573fda6.pdf