Identification of nonlinear differential equations via Fourier series operational matrix for repeated integration
The problem of the identification of nonlinear first-order and second- order differential equations is solved using the Fourier series. The proposed method consists of reducing the identification problems into a set of linear algebraic equations by expanding the candidate functions as a Fourier series with unknown coefficients; the operational matrix for integration, and one shot operational matrix for repeated integration are used to evaluate the integrals. This approach has advantages mainly due to the use of sinusoidal functions. The method can be extended to any order of nonlinear differential equations. Some examples are used to demonstrate the application of the proposed method.
scientific article; zbMATH DE number 753903
scientific article