Search

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. The proposed approach is based on an Unsupervised Combined Artificial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks containing adjustable parameters (the weights and biases); results are then optimized with the combined neural network. The proposed method is tested on series of Lane-Emden differential equations and the results are reported. Afterward, these results are compared with the solution of other methods demonstrating the efficiency and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we provide the collocation method for natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear waste disposal. This problem is a non-linear, three-point boundary value problem on semi-infinite interval. We use two orthogonal functions namely rational Gegenbauer and modified generalized Laguerre functions which are defined as basis functions in this approach and compare them together. We also present the comparison of these works with Runge-Kutta solution, moreover, in the graph of the ||Res||², we show that the present solutions are accurate and applicable. [ABSTRACT FROM AUTHOR]