In this research, the well-known non-linear Lane–Emden–Fowler LEF equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.
['Junaid Ali Khan', 'Muhammad Asif Zahoor Raja', 'Mohammad Mehdi Rashidi', 'Muhammad Ibrahim Syam', 'A.M. Wazwaz']
Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory