The Numerical Solution of Nonlinear Fractional Lienard and Duffing Equations Using Orthogonal Perceptron
[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee
2023
scientific article
english
- orthogonal neural network
- simulated annealing optimization technique
- fractional differential equations
- Caputo derivative
EN This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the oscillating circuit and generalize the spring–mass device equation. The proposed approach transforms the given nonlinear fractional differential equation (FDE) into an unconstrained minimization problem. The simulated annealing (SA) algorithm minimizes the mean square error. The proposed techniques examine various non-integer order problems to verify the theoretical results. The numerical results show that the proposed approach yields better results than existing methods.
13.09.2023
1753-1 - 1753-19
Article Number: 1753
CC BY (attribution alone)
open journal
final published version
at the time of publication
70
2,2