NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS THROUGH THE LAGUERRE NEURAL NETWORK

The Chebyshev and legendre neural networks developed to approximate the solution of ordinary differential equations were adapted to the numerical solution of a partial differential equation, but using Laguerre's orthogonal polynomial, which has been called by the authors as Laguerre Neural Network (LNN). The Laguerre Neural Network consists of a single neural layer and an input pattern expansion using Laguerre polynomials. LNN has been applied to solve a Poisson partial differential equation with Dirichlet boundary conditions. A comparison of the solution by LNN with the analytical solution of the equation has been perfomed. The result has been showed a great(using what measure??) approximation of the solution by the Laguerre Neural Network with the training of the network in a reduced number of times compared to the multilayer perceptron network.