A numerical approach for a class of astrophysics equations using piecewise spectral-variational iteration method

Abstract

PurposeThe main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.Design/methodology/approachThis method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.FindingsSome well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.Originality/valueIn this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.