Numerical solution of system of Emden-Fowler type equations by Bernstein collocation method

Abstract

The system of Emden-Fowler equations occurs frequently in physical and natural sciences. These system of equations are very difficult to handle due to their singularity and the nonlinearity. We provide a numerically robust technique for approximating the solution of the system of Emden-Fowler equations. This algorithm is based on the Bernstein polynomial accompanied by the collocation method. First, we transform the system of Emden-Fowler equations into their integral form. Then we implement the Bernstein polynomial approximation and the collocation technique to acquire a nonlinear system of equations. We apply the Newton-Raphson method to analyze the resulting nonlinear system of equations. We also discuss the error analysis of this method. We provide the numerical results of the $$L_{\infty }$$ error, the $$L_{2}$$ -norm error, and the residual error of some numerical supporting problems to examine the accuracy of the current technique. The advantage of the present method is exhibited by comparing the numerical results obtained by the proposed technique and other known techniques.