A new rational Legendre neural network for solving the Blasius equation

In this paper, we present a novel artificial neural network framework for solving the Blasius equation, a nonlinear ordinary differential equation defined on a semi-infinite domain. Our experiments revealed that traditional activation functions, such as Tanh and ReLU, did not produce satisfactory results. To address this, we employed custom activation functions based on Rational Legendre polynomials, which demonstrated superior performance in approximating the solution. The results highlight the effectiveness and potential of this approach, offering a valuable contribution to the scientific community for addressing similar nonlinear differential equations.

کلیدواژه ها:

The Blasius equation ، Rational Legendre polynomials ، Neural Network ، Boundary-layer flow ، Semi-infinite domains ، Nonlinear differential equations