Posts by Călin-Ioan Gheorghiu


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.


C.I. Gheorghiu
“Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Acdemy


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, Journal of Physics A: Mathematical and Theoretical, 56 (2023) no. 17, LT01,


About this paper


Journal of Physics A: Mathematical and Theoretical

Publisher Name

IOP Publishing Ltd.

Print ISSN


Online ISSN


google scholar link

[1] Iacono R 2008 J. Phys. A: Math. Theor. 41 455204
[2] O’Regan D 1996 Can. J. Math. 48 143
[3] Boyd J P 2013 J. Comput. Appl. Math. 244 90
[4] Delkhosh M and Parand K 2019 Hacettepe J. Math. Stat. 48 1601
[5] Shen J, Tang T and Wang L – L 2011 Spectral Methods. Algorithms, Analysis and Applications (Berlin: Springer) ch 7
[6] Weidemann J A C and Reddy S C 2000 ACM Trans. Math. Softw. 26 465
[7] Boyd J P 2000 Chebyshev and Fourier Spectral Methods (New York: Dover) p 11501
[8] Gheorghiu C I 2014 Spectral Methods for Non-Standard Eigenvalue Problems. Fluid and Structural Mechanics and Beyoud (Berlin: Springer) ch 3 and 4
[9] Tretehten L N, Birkisson A and Driscoll T A 2018 Exploring ODEs (Philadelphia, PA:SIAM)

Related Posts

Finite Element Method and Applications

Book summarySummary of the book… Book cover Contents clickableIntroduction by Acad. Caius Iacob Foreword Functional Analysis Itinerary 1.1. Vector spaces.…