Approximation of functions and approximate solution of partial differential equations using radial basis functions networks

The application of radial basis function networks for approximating functions and solving partial differential equations has investigated. Fast gradient first-order methods and an algorithm of the Levenberg-Marquardt method for learning networks using radial basis functions have developed. The proposed algorithms are using an analytical calculation of the gradient vector of the functional error and the Jacobi matrix. Experiments showed that algorithms based on first-order methods provide low accuracy and require a lot of network learning time. Only the developed algorithm of the Levenberg-Marquardt method has ensured high approximation accuracy of the complicated functions of many variables and the solution of partial differential equations.