Stochastic numerical treatment for solving Falkner–Skan equations using feedforward neural networks

• Main Authors: Ahmad, Iftikhar, Ahmad, Siraj-ul-Islam, Bilal, Muhammad Qamar, Anwar, Nabeela
• Format: Article
• Language: English; English
• Published: Springer London 2017
• Subjects: GA Mathematical geography. Cartography
• Online Access: http://umpir.ump.edu.my/id/eprint/20424/1/Stochastic%20Numerical%20Treatment%20for%20Solving%20Falkner%E2%80%93Skan%20Equations%20Using%20Feedforward%20Neural%20Networks.pdf; http://umpir.ump.edu.my/id/eprint/20424/2/Stochastic%20Numerical%20Treatment%20for%20Solving%20Falkner%E2%80%93Skan%20Equations%20Using%20Feedforward%20Neural%20Networks%201.pdf; http://umpir.ump.edu.my/id/eprint/20424/; https://link.springer.com/article/10.1007/s00521-016-2427-0

In this article, the artificial intelligence techniques have been used for the solution of Falkner–Skan (FS) equations based on neural networks optimized with three methods including active set technique, sequential quadratic programming and genetic algorithms (GA) hybridization. Log-sigmoid activation function is used in artificial neural network architecture. The proposed techniques are applied to a number of cases for Falkner–Skan problems, and results were compared with GA hybrid results in all cases and were found accurate. The level of accuracy is examined through statistical analyses based on a sufficiently large number of independent runs.