Numerical results of Emden-Fowler boundary value problems with derivative dependence using the Bernstein collocation method

In this paper, we propose an efficient numerical technique based on the Bernstein polynomials for the numerical solution of the equivalent integral form of the derivative dependent Emden-Fowler boundary value problems which arises in various fields of applied mathematics, physical and chemical sciences. The Bernstein collocation method is used to convert the integral equation into a system of nonlinear equations. This system is then solved efficiently by suitable iterative method. The error analysis of the present method is discussed. The accuracy of the proposed method is examined by calculating the maximum absolute error and the L-2 error of four examples. The obtained numerical results are compared with the results obtained by the other known techniques.

Automated summary

This paper proposes an efficient numerical technique based on the Bernstein polynomials for the numerical solution of the derivative dependent Emden-Fowler boundary value problems. By converting the integral equation into a system of nonlinear equations using the Bernstein collocation method and solving it efficiently with a suitable iterative method, accurate numerical solutions are obtained. The method is analyzed for error and compared with other known techniques.