A New Approach for Solving Nonlinear Thomas-fermi Equation Based on Fractional Order of Rational Bessel Functions
نویسندگان
چکیده
In this article, we introduce a fractional order of rational Bessel functions collocation method (FRBC) for solving the Thomas-Fermi equation. The problem is defined in the semi-infinite domain and has a singularity at x = 0 and its boundary condition occurs at infinity. We solve the problem on the semi-infinite domain without any domain truncation or transformation of the domain of the problem to a finite domain. This approach at first, obtains a sequence of linear differential equations by using the quasilinearization method (QLM), then at each iteration the equation is solves by FRBC method. To illustrate the reliability of this work, we compare the numerical results of the present method with some well-known results, to show that the new method is accurate, efficient and applicable.
منابع مشابه
A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...
متن کاملApplication of fractional-order Bernoulli functions for solving fractional Riccati differential equation
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration...
متن کاملNumerical approach for solving a class of nonlinear fractional differential equation
It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equation. The fractional derivatives are described...
متن کاملSimplest Equation Method for nonlinear solitary waves in Thomas- Fermi plasmas
The Thomas-Fermi (TF) equation has proved to beuseful for the treatment of many physical phenomena. In this pa-per, the traveling wave solutions of the KdV equation is investi-gated by the simplest equation method. Also, the effect of differentparameters on these solitary waves is considered. The numericalresults is conformed the good accuracy of presented method.
متن کاملRational Chebyshev Collocation approach in the solution of the axisymmetric stagnation flow on a circular cylinder
In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...
متن کامل