Legendre wavelets method for solving differential equations of Lane–Emden type

A numerical method for solving the Lane–Emden equations as singular initial value problems is presented. Using integral operator and convert Lane–Emden equations to integral equations and then applying Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties together with the Gaussian integration method are then utilized to reduce the integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.