Numerical solution of coupled Lane-Emden boundary value problems using
the Bernstein collocation method
Abstract
In this paper, we provide an efficient numerical technique based on the
Bernstein polynomials for numerical approximation of the coupled
Lane-Emden type equation which arises in various fields of applied
mathematics, physical and chemical sciences. We consider the equivalent
integral form of the coupled Lane-Emden boundary value problems. 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
current method is discussed. The accuracy of the proposed method is
examined by calculating the maximum absolute error
$L_{\infty}$, the $L_{2}$ error and the
residual error of some numerical examples. The obtained numerical
results are compared with the exact solutions and the results obtained
by the other known techniques.