We consider a class of singular systems of Lane-Emden type      ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...

We have derived exact solutions of the isothermal Lane–Emden equation with and without rotation in a cylindrical geometry. The corresponding hydrostatic equilibria are relevant to the dynamics of the solar nebula before and during the stages of planet and satellite formation. The nonrotating solution for the mass density is analytic, nonsingular, monotonically decreasing with radius, and it sat...

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...

In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed.

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area...

The four nominal species currently included in the anthomyiid genus Chirosiomima Hennig, 1966 are critically assessed and redescribed. It is shown that the type species of Chirosiomima was originally misidentified. Chirosiomima obscurinervis (Emden, 1941) is resurrected from synonymy of C. gestroi (Séguy, 1930). Chirosiomima collini Ackland, 1968 is transferred to Botanophila Lioy (comb. nov.) ...