An effective scheme for solving a class of nonlinear doubly singular boundary value problems through quasilinearization approach

Abstract

In this paper, an effective analytical method is introduced for solving a class of two-point nonlinear doubly singular boundary value problems (SBVPs) arising in various physical models. The method is the combination of Newton’s quasilinearization and Picard iteration method in which quasilinearization is utilized to reduce the nonlinear doubly SBVPs to a sequence of linear problems and then the Picard iteration method is used to obtain the approximate analytical solutions of linearized equations arising from quasilinearization method. The convergence analysis of the method is also discussed. To demonstrate the efficiency of the method, we consider various numerical examples arising in physical models including real-life problems. The numerical simulations justify the superiority and high performance of the method and the obtained results are compared with some other existing schemes. The comparisons reveal the applicability and effectiveness of the present work. The method also works quite efficiently for other nonlinear boundary value problems of any order. The method is successfully applied on second and third–order regular boundary value problems and the results are compared with the existing methods.