Haar wavelets collocation on a class of Emden-Fowler equation via Newton's quasilinearization and Newton-Raphson techniques
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In this paper we have considered generalized Emden-Fowler equation, y”(t)+σ t^γ y^β(t)=0, t ∈ ]0,1[ subject to the following boundary conditions y(0)=1, y(1)=0; & y(0)=1, y'(1)=y(1), where γ,β and σ are real numbers, γ<-2, β>1. We propsoed to solve the above BVPs with the aid of Haar wavelet coupled with quasilinearization approach as well as Newton-Raphson approach. We have also considered the special case of Emden-Fowler equation (σ=-1,γ=-1/2 and β=3/2) which is popularly, known as Thomas-Fermi equation. We have analysed different cases of generalised Emden-Fowler equation and for compared our results with existing results in literature. We observe that small perturbations in initial guesses does not affect the the final solution significantly.
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