Bernoulli collocation method for the third-order Lane-Emden-Fowler boundary value problem

Abstract

We propose two efficient numerical algorithms, Bernoulli uniform collocation method and Bernoulli Chebyshev collocation method for solving 3rd-order Lane-Emden-Fowler boundary value problems. To avoid singularity at x=0, we transform the concerned problem into its integral form. By using the Bernoulli collocation method, the resulting integral equation is converted into a system of nonlinear equations to be solved numerically by any suitable iteration method. The error bound of the algorithm and the existence of a unique solution of the problem are also discussed. The high accuracy and efficiency of the proposed method are shown by comparing the results of L∞ and L2 errors of several examples. Moreover, the numerical results of our method are compared with the results obtained by the other known techniques.