2019/11/13 by Amit K. Verma, Narendra Kumar, Verma, Amit Kumar +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #34B15 #34B16 #42C40 #Elasticity and Wave Propagation #FOS: Mathematics #Fractional Differential Equations Solutions #Image and Signal Denoising Methods #Iterative Methods for Nonlinear Equations #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1911.05819
openalex publication_date 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we have considered generalized Emden-Fowler equation,\n\y''(t)+
sigma t^
gamma y^
beta(t)=0, ~~~~~~~~t
in ]0,1[\n subject to the following boundary conditions ny(0)=1,~y(1)=0;~~
amp;~~y(0)=1,~y'(1)=y(1), where \γ,\β\nand \σ are real numbers, \γ<-2, \β>1. We propsoed to solve the\nabove BVPs with the aid of Haar wavelet coupled with quasilinearization\napproach as well as Newton-Raphson approach. We have also considered the\nspecial case of Emden-Fowler equation (\σ=-1,\γ=\(-1)/(2) and\n\β=\(3)/(2)) which is popularly, known as Thomas-Fermi equation. We\nhave analysed different cases of generalised Emden-Fowler equation and compared\nour results with existing results in literature. We observe that small\nperturbations in initial guesses does not affect the the final solution\nsignificantly.\n