فهرست مطالب

Computational Methods for Differential Equations
Volume:3 Issue: 1, Winter 2015

  • تاریخ انتشار: 1393/10/11
  • تعداد عناوین: 6
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  • Razie Shafeii Lashkarian *, Dariush Behmardi Sharifabad Pages 1-13
    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.
    Keywords: Monodromy problem, degenerate critical point, hyperbolic critical point, nilpotent critical point, blow up method
  • Hammad Khalil *, Rahmat Khan, M. Rashidi Pages 14-35
    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.
    Keywords: Brenstien polynomials, Coupled system, Fractional differential equations, operational matrices of integrations, Numerical simulations
  • Mahdiye Gholipour, Payam Mokhtary * Pages 36-44
    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.
    Keywords: Discrete Galerkin method, Generalized Jacobi polynomials, Higher even-order Integro-Differential Equations
  • Hossein Bevrani * Pages 45-50
    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.
    Keywords: Ordinary differential equations, Probability density functions, Pearson's family distribution
  • Tahereh Eftekhari * Pages 51-58
    ‎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.
    Keywords: Nonlinear equations‎, ‎Ostrowski's method‎, ‎Order of convergence‎, ‎Efficiency index
  • Md. Nur Alam *, Md. Mashiar Rahman, Md. Rafiqul Islam, Harun Or Roshid Pages 59-69

    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.

    Keywords: New extended (G', G)-expansion method, the Benjamin-Ono equation, Exact solutions