## Abstract

We solve numerically the nonlinear and double singular boundary value problem formed by the well known Emden-Fowler equation \(u^{\prime\prime}=u^{s}x^{-1/2},s>1\) along with the boundary conditions \(u(0)=1\) and \(u(\infty)=0\). In order to capture the exponential decrease of its solution we use the Laguerre-Gauss-Radau collocation method and infer its convergence. We show that the value of \(u^{\prime}\) at origin, which plays a fundamental role in these problems, definitely satisfies some rigorous accepted bounds. A particular attention is paid to the Thomas-Fermi case, i.e. \(s:=3/2\). We treat the problems as boundary values ones without any involvement of ones with initial values. The method is robust with respect to scaling and order of approximation.

## Authors

C.I. **Gheorghiu**

“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Acdemy

## Keywords

Emden-Fowler problem; Laguerre collocation; slope in origin; bounds

## Paper coordinates

C.I. Gheorghiu, *Accurate Laguerre collocation solutions to a class of Emden–Fowler type BVP, * ,

## About this paper

##### Journal

Journal of Physics A: Mathematical and Theoretical

##### Publisher Name

IOP Publishing Ltd.

##### Print ISSN

17518113

##### Online ISSN

17518121

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