I.S Kolbin, D.L. Reviznikov

In this article we discuss a method for solving boundary value problems for equations of mathematical physics. The method is based on neural network modeling. Networks of normalized radial basis functions are proposed as approximating neural network models. In this article we discuss solutions of stationary (elliptic) and non-stationary (parabolic) problems. The algorithm for the solution is to minimize the mean-square functional error arising from the substitution of neural network model in differential equation and boundary conditions. The hybrid algorithm with neural network spatial approximation and finite-difference time-splitting is used for solving time-dependent problems. For the representative set of test problems the analysis of the dependence of the error and the size of neural network was made. The methods have proved effective according to the results of the calculations