Extrapolation of Duffing Equation Solution by Using RBF Network - Tatyana Lazovskaya; Galina Malykhina; Dmitry Pashkovsky; Dmitry Tarkhov (Современные информационные технологии и IT-образование, 2021)
The article considers the problem of approximation of the solution of the Cauchy problem for an ordinary differential equation of the second order. The approximation scheme is based on the Taylor expansion of the solution with a remainder in the Lagrange form. The residual term is sought in the form of the output of a neural network with radial basis functions (RBF networks). An algorithm for learning (choosing the optimal parameters) of the RBF network is presented. Using the example of solving the Cauchy problem for a second-order nonlinear differential equation – the Duffing oscillator, the influence of various radial-basis functions on the quality of interpolation and extrapolation of the solution to the Duffing equation is investigated.