Solving Falkner-Skan type equations via Legendre and Chebyshev Neural
  Blocks
Alireza Afzal Aghaei Kourosh Parand Ali Nikkhah Shakila Jaberi
In this paper, a new deep-learning architecture for solving the non-linear
Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks,
this approach shows how orthogonal polynomials can be used in neural networks
to increase the approximation capability of artificial neural networks. In
addition, utilizing the mathematical properties of these functions, we overcome
the computational complexity of the backpropagation algorithm by using the
operational matrices of the derivative. The efficiency of the proposed method
is carried out by simulating various configurations of the Falkner-Skan
equation.