Bernoulli wavelets functional matrix technique for a system of nonlinear singular Lane Emden equations

Abstract

In the present paper, we developed the functional matrix of integration via Bernoulli wavelets and generated a competent numerical scheme to solve the nonlinear system of singular differential equations which is Lane Emden form by Bernoulli wavelets collocation technique (BWCT) with different physical conditions. The system of nonlinear singular models is not smooth to operate as they are singular and nonlinear. This approach obtains the solution for this system by transforming it into a-nonlinear system of algebraic equations by expanding through Bernoulli wavelets with unknown coefficients. These unknown coefficients are calculated using the collocation scheme. The consistency and proficiency of the developed approach are demonstrated via graphs and tables. Attained results confirm that the newly implemented approach is more effective and accurate than other techniques which are available in the literature. All computations have been made using Mathematica software. The convergence of this method is explained in terms of theorems.