Accurate Laguerre collocation solutions to a class of Emden–Fowler type BVP


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

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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,


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Journal of Physics A: Mathematical and Theoretical

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IOP Publishing Ltd.

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