Higher resolution methods based on quasilinearization and Haar wavelets on Lane–Emden equations

Abstract

Computing solutions of singular differential equations has always been a challenge as near the point of singularity it is extremely difficult to capture the solution. In this research paper, Haar wavelet coupled with quasilinearization approach (HWQA) is proposed for computing numerical solution of nonlinear SBVPs popularly also referred as Lane–Emden equations. This technique is the combination of quasilinearization and Haar wavelet collocation method. To show the accuracy of the HWQA, several examples are presented. Convergence of the proposed method is also established in this paper, which shows that proposed method converges very fast.