Numerical study on Lane-Emden type equation using Bessel Artificial Neural Network approach

The present paper introduces a new Bessel Artificial Neural Network (BeNN) approach to solve non-homogeneous Lane-Emden type equation, which are second order non-linear singular initial value ordinary differential problem. A single layer Feed-Forward Neural Network as unsupervised method is utilized and the hidden layer is removed by using a series expansion of Bessel polynomials. We also applied the error back propagation learning algorithm for minimizing the computed Mean Square Error (MSE) function and amending the Neural Network parameters (weights) without direct utilize of other optimization methods. In terms of accuracy and efficiency of the present learning approach by a few basis of Bessel polynomials, the obtained outcomes are compared with exact solution and some other numerical results.

Keywords:

Bessel Neural Network , Feed forward Neural Network , Error back Propagation method , singular initial value problem