A New Bernoulli Wavelet Operational Matrix of Derivative Method for the Solution of Nonlinear Singular Lane–Emden Type Equations Arising in Astrophysics

Abstract

In this paper, a new method is presented for solving generalized nonlinear singular Lane–Emden type equations arising in the field of astrophysics, by introducing Bernoulli wavelet operational matrix of derivative (BWOMD). Bernoulli wavelet expansions together with this operational matrix method, by taking suitable collocation points, converts the given Lane–Emden type equations into a system of algebraic equations. Solution to the problem is identified by solving this system of equations. Further applicability and simplicity of the proposed method has been demonstrated by some examples and comparison with other recent methods. The obtained results guarantee that the proposed BWOMD method provides the good approximate solution to the generalized nonlinear singular Lane–Emden type equations.