Numerical solution of the controlled Duffing oscillator by the pseudospectral method (Q1893560)

The authors introduce a new direct numerical method for solving the controlled Duffing oscillator. The method is based on a pseudospectral method in which the authors construct the \(m\)th degree interpolation polynomials using the Legendre-Gauss-Lobatto collocation points to approximate the state and control functions. With this method, the system dynamics, initial conditions and the integral expression are converted to a system of algebraic equations that can be solved for the unknown coefficients by the iterative Newton method. Finally, numerical results are presented and a comparison is made with an existing method of Chebyshev approximation to demonstrate the efficiency and the accuracy of the proposed numerical method.