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

Abstract

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.

Integrated intelligent Jaya Runge-Kutta method for solving Falkner-Skan equations for Various Wedge Angles

“…In addition, for acceleration flows, we can observe that as the parameter β increases, the boundary layer thickness increases, and eventually tends to one as the distance increases from the initial boundary. η df/dη To be more specific, two classic cases Hiemenz flow and Homann axisymmetric stagnation flow, are in comparison with Jaya, PSO, Hyperband, GA, and the reference solution [36]. In Tables 5, the results obtained with Jaya method agrees pretty well with the reference solution [36].…”

“…10 shows the graph of stream function f (η), its velocity and skin friction coefficient gained with Jaya optimization method. From Table . 5, the solutions from different optimization methods including Jaya, PSO, Hyperband and GA are compared with the reference solution [36]. Still our method obtains the most agreeable results.…”

“…The numerical results for the stream function f , velocity profile f , and skin friction coefficient f are illustrated for specific flow problems. The velocity profile along the coordinates are compared with reference solutions from [36], to show the accuracy of present method compared with other robust optimization methods.…”

“…For different coefficients β and β 0 , the Falkner-Skan problem can be divided into the following four categories: )XQFWLRQYDOXH In this case, Falkner-Skan equation is known as Blasius equation. The solution is obtained using the Runge-Kutta method integrated with the Jaya algorithm, the PSO algoritm, the Hyperband algorithm, the GA and reference solution from [36]. First, the convergence history graph of the fitness function over 100 iterations is presented in Figure 6.…”

Heuristic computational intelligence approach to solve nonlinear multiple singularity problem of sixth Painlev́e equation

“…The suitable combination of these above equations can be used to model the differential equations like (5-7), for reader interest see more references like [46,47] and [48].…”