A new polynomial-time algorithm for linear programming
Combinatorica
Primal-dual interior-point methods
Primal-dual interior-point methods
Computers & Mathematics with Applications
Solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method
Computers & Mathematics with Applications
Application of homotopy analysis method to solve MHD Jeffery-Hamel flows in non-parallel walls
Advances in Engineering Software
Homotopy perturbation method for nonlinear MHD Jeffery-Hamel problem
Computers & Mathematics with Applications
A new stochastic approach for solution of Riccati differential equation of fractional order
Annals of Mathematics and Artificial Intelligence
Numerical treatment of nonlinear Emden---Fowler equation using stochastic technique
Annals of Mathematics and Artificial Intelligence
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In this paper new computational intelligence techniques have been developed for the nonlinear magnetohydrodynamics (MHD) Jeffery-Hamel flow problem using three different feed-forward artificial neural networks trained with an interior point method. The governing equation for the two-dimensional MHD Jeffery-Hamel flow problem is transformed into an equivalent third order nonlinear ordinary differential equation. Three neural network models using log-sigmoid, radial basis and tan-sigmoid activation functions are developed for the transformed equation in an unsupervised manner. The training of weights of each neural network is carried out with an interior point method. The proposed models are evaluated on different variants of the Jeffery-Hamel problem by varying the Reynolds number, angles of the walls and the Hartmann number. The accuracy, convergence and effectiveness of the designed models are validated through statistical analyses based on a sufficiently large number of independent runs. Comparative studies of the proposed solutions with standard numerical results, as well as recently reported solutions of analytic solvers illustrate the worth of the proposed solvers.