An efficient recursive technique with Padé approximation for a kind of Lane–Emden type equations emerging in various physical phenomena

Abstract

The study numerically examined a class of nonlinear singular differential problems known as the Lane–Emden differential equation, which emerges in numerous real-world situations. The primary goal of this work is to formulate a computationally efficient iterative technique for solving the nonlinear Lane–Emden initial value problems. The proposed approach is a hybrid of the homotopy perturbation method and the Padé approximation. The nonlinear singular Lane–Emden initial value problem (SLEIVP) is transformed into an equivalent recursive integral employing the Picard’s approach. To resolve the singularity and nonlinearity, the recursive integral equation is transformed into a system of integral equations by using the homotopy notion. Furthermore, to enhance the convergence rate of the technique, Padé approximation is taken into account. The convergence analysis for the proposed approach is also conducted. The present technique is tested on SLEIVPs and numerical findings are compared with the existing techniques, to demonstrate the accuracy, effectiveness and ease of use.