Application of the neural network for solution of the Sturm-Liouville boundary value problems. (Ukrainian. English summary) Zbl 1091.65083
Summary: This article deals with an application of a neural network to the solution of boundary value problems of mathematical physics. The neural network is integrated into the finite element method to get an almost exact solution. An example of the solution of a one-dimensional Sturm-Liouville boundary value problem is presented. The main attention is paid to research of the network structure and training sets.
MSC:
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
