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

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 L0.0 and L2 errors of several examples. Moreover, the numerical results of our method are compared with the results obtained by the other known techniques.

Automated summary

Two efficient numerical algorithms, Bernoulli uniform collocation method and Bernoulli Chebyshev collocation method, are proposed for solving 3rd-order Lane-Emden-Fowler boundary value problems. The singularity at x = 0 is avoided by transforming the 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. The high accuracy and efficiency of the proposed method are demonstrated by comparing the results with other known techniques.