We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and perfor...

<p style='text-indent:20px;'>Ordinary differential equations are converted into a constrained optimization problems to find their approximate solutions. In this work, an algorithm is proposed by applying particle swarm (PSO) solution of ODEs based on expansion approximation. Since many cases linear and nonlinear have singularity point, Padé approximant which fractional employed for more a...

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some ...

We classify finite Morse index solutions of the following nonlocal Lane-Emden equation (−∆)u = |u|p−1u R for 1 < s < 2 via a novel monotonicity formula. For local cases s = 1 and s = 2 this classification is provided by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case 0 < s < 1 finite Morse index solutions are classified by Davila, Dupaigne...

The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obt...

We are concerned with the Lane-Emden problem{−Δu=upinΩ,u>0inΩ,u=0on∂Ω, where Ω⊂R2 is a smooth bounded domain and p>1 sufficiently large. Improving some known asymptotic estimates on solutions, we prove non-degeneracy local uniqueness of multi-spikes positive solutions for general domains. Our methods mainly use ODE's theory, various Pohozaev identities, blow-up analysis properties Green's funct...

The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...