A new efficient semi-numerical method with a convergence control parameter for Lane–Emden–Fowler boundary value problem

Abstract

We propose a new efficient semi-numerical method for solving the Lane–Emden–Fowler type equations that arise in various scientific applications. To avoid singular behavior at t=0, we convert our problem into an integral equation before establishing the recursive procedure for resolving the problem. Unlike the existing methods, the current approach does not require the calculation of the transcendental equations for the unknown coefficients. The existence of a unique solution to the problem is discussed in detail. A convergence parameter ħ is introduced to control the convergence and the rate of convergence of the method. Moreover, the convergence analysis of the current method is discussed. Several mathematical and physical examples are selected from the open literature whose exact solutions are unknown to check the new scheme’s accuracy and applicability. The present method gives a convergent series solution, whereas the ADM (Singh and Kumar, 2014) fails to provide a convergent solution. The new approach resolves the issue of the existing method, which allows only capturing the solutions for the smaller domain of the solution.