Implementation of LCDNN for solving the General Falkner-Skan equation

This repository contains the implementation of the method which is presented in the following paper:

Solving non-linear boundary value problems of Falkner-Skan type equations via Legendre and Chebyshev Neural Blocks

It introduces Legendre and Chebyshev Blocks to solve the general falkner-skan equation.

Falkner-Skan Equation

General form:

f''' + α ff'' + β(1 - (f')^2) = 0

with boundary conditions:

f(0) = f'(0) = 0,  and  f'(∞) = 1

Standard Flows

• Blasius-Flow:

  • α = 0.5 , β = 0

• Pohlhausen-Flow:

  • α = 0, β = 1

• Homann-Flow:

  • α = 2, β = 1

• Hiemenz-Flow:

  • α = 1, β = 1

• Hastings-Flow:

  • α = 1, β ∈ [-0.18, 2]

• Craven-Flow:

  • α = 1, β ∈ [10, 40]

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