Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

in this work g'/g-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. it is shown that g'/g-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

2 Distance from a Point to an Ellipse 3 2.1 The Closest Point’s Normal is Directed Toward the Query Point . . . . . . . . . . . . . . . . 3 2.2 The Case of a Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 The Query Point is the Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 The Query Point is on the Vertical A...

this paper presents the application of the matching pursuit method to model synchronous generator. this method is useful for online analysis. in the proposed method, the field voltage is considered as input signal, while the terminal voltage and active power of the generator are output signals. usually, the difference equation with a second degree polynomial structure is used to estimate the co...

In recent years multigrid methods have been proven to be very e cient for solving large systems of linear equations resulting from the discretization of positive de nite di erential equations by either the nite di erence method or the h-version of the nite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which ar...

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.

this paper studies the generalized version of thezakharov-kuznetsov benjamin-bona-mahoney equation. the functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. there are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. the results of this pape...

We study dynamic Bertrand mean field games (MFG) with exhaustible capacities in which companies compete with each other using the price as the strategic variable and the interaction among the competition is through the average price. We consider both continuum mean field games and finite player games. Dynamic continuum mean field games can be modeled as a system of partial differential equation...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...