A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane-Emden equations

摘要

In this research, we present an iterative spectral method for the approximate solution of a class of Lane-Emden equations. In this procedure, we initially extend the Legendre wavelet which is appropriate for any time interval. Thereafter, the Guass-Legendre collection points of the Legendre wavelet are acquired. Employing this new approach, the iterative spectral technique converts the differential equation to a set of algebraic equations which diminishes the computational costs effectively. By solving the obtained algebraic equations, an accurate approximate solution for the assumed Lane-Emden equation is achieved. The present technique is validated by solving a number of Lane-Emden problems and are compared with other existing methods. The numerical simulations demonstrate that the new algorithm is simple and it has highly accuracy.