Numerical Treatment of Lane-Emden Type Equation via Wavelet Scheme with Equal Collocation Points

This research explains the Haar wavelet method to approximate the Lane-Emden type problems that arises in astrophysics. Following that, a numerical technique is described for fast computation of the Haar functions. The Haar wavelet approach is then examines the experimental framework of the Haar wavelet approach and compares it to the Homotopy perturbation method and the existing methods. The purpose of this study is to provide a Haar wavelet approach for the numerical study of Lane-Emden type equations. As proved by the tested examples, certain well-known classes of Lane-Emden type equations are solved to show the precision of present method. The study proposes a new solution algorithm for any analytic system for the generalized Lane-Emden equation. The wavelet scheme outperforms the Homotopy perturbation method, the neural network method when computed using the present numerical methodology.