Haar wavelet collocation method for Lane–Emden equations with Dirichlet, Neumann and Neumann–Robin boundary conditions

Abstract

In this paper, we present a numerically stable algorithm based on the Haar wavelet collocation method (hwcm) for numerical solution of a class of Lane–Emden equation with Dirichlet, Neumann and Neumann–Robin type boundary conditions, arising in various physical models. The Haar wavelet collocation method uses simple box functions and hence the formulation of the numerical algorithm is straightforward. Unlike other methods, the hwcm can be applied easily and accurately to the Neumann type boundary conditions. The advantage of the Haar wavelet method is its efficiency and simple applicability for a variety of boundary conditions. The Haar wavelet collocation method is utilized to reduce the Lane–Emden equation with boundary conditions to a system of algebraic equations, then the Newton’s method is employed for numerical solutions. Nine examples of the Lane–Emden equation with various types of boundary conditions are provided to demonstrate the accuracy and efficiency of the hwcm. The numerical results are compared with the results obtained by other techniques and the exact solution.