Nature-inspired computing approach for solving non-linear singular Emden-Fowler problem arising in electromagnetic theory

作者：Khan Junaid Ali; Raja Muhammad Asif Zahoor^*; Rashidi Mohammad Mehdi; Syam Muhammad Ibrahim; Wazwaz Abdul Majid

来源：Connection Science, 2015, 27(4): 377-396.

DOI：10.1080/09540091.2015.1092499

• computational intelligence
• neural networks
• particle swarm optimisation
• pattern search
• interior-point method
• hybrid computing
• singular initial value problems

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.

• 出版日期2015-10-2