Article history: Received 28 May 2010 Available online 16 September 2010 Submitted by Goong Chen

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...

In this article, we present a collocation method for second-order nonlinear Lane-Emden type pantograph differential equations under intial conditions. According to the method, solution of problem is sought depending on Pell-Lucas polynomials. The polynomials are written in matrix form based standard bases. Then, and its derivatives also forms. Next, transformation constituted proportion delay f...

We prove that positive solutions of the superlinear Lane–Emden system in a two-dimensional smooth bounded domain are independently exponents system, provided comparable. As consequence, energy is uniformly bounded, crucial information their asymptotic study. In addition, boundedness may fail if not

The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the ...

In this article Differential Transformation Method (DTMs) is considered to find exact and approximate solutions of singular Initial Value Problems (IVPs) of the Lane-Emden type in second-order Ordinary Differential Equations (ODEs). The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series so...

1 School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China 2 Department of Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China 3 School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, SA 5005, Australia 4 School of Engineering and Science, Victoria University, Melbourne, VIC 8001, Austr...

We establish some bifurcation results for the boundary value problem −∆u = g(u) + λ|∇u| + μf(x, u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in R , λ, μ ≥ 0, 0 < p ≤ 2, f is nondecreasing with respect to the second variable, and g is unbounded around the origin. The asymptotic behaviour of the solution around the bifurcation point is also established, provided g(u) behav...