Haar wavelets collocation on a class of Emden-Fowler equation via Newton's quasilinearization and Newton-Raphson techniques
share
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.
READ FULL TEXT