An efficient approximation method for nonlinear singular value problems arising in astrophysics: an operational matrix approach

Abstract

In this paper, an efficient wavelet-based algorithm is introduced to investigate the approximate solutions for a few nonlinear singular initial value problems arising in astrophysics. Ultraspherical wavelet method (USWM) is utilized for solving the Lane-Emden type equations. The proposed method is utilized to convert the given nonlinear singular value differential equations into a system of algebraic equations using operational matrices of derivatives. Convergence analysis of the method is discussed. The obtained solutions are compared with LWM, CWM and exact solutions. A few numerical experiments are given to demonstrate the accuracy and efficiency of the proposed method. Satisfactory agreement with exact and other numerical solutions is observed. The efficiency of the proposed method is confirmed by means of computational CPU runtime. Moreover, the use of USWM is investigated to be simple, accurate and less computational cost.