Identification of nonlinear differential equations via Fourier series operational matrix for repeated integration
type: Item
instance of: scholarly article
title: Identification of nonlinear differential equations via Fourier series operational matrix for repeated integration
zbMATH Open document ID: 0821.65050
DOI: 10.1016/0096-3003(94)00093-J
author: Yanyan Li
published in: Applied Mathematics and Computation
publication date: 1995-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 753903
zbMATH Keywords: Fourier series expansion
zbMATH Keywords: least squares method
zbMATH Keywords: numerical examples
zbMATH Keywords: identification problems
zbMATH Keywords: operational matrix
zbMATH Keywords: nonlinear differential equations
reviewed by: Dana Petcu
MaRDI profile type: Publication
cites work: Optimal control of delay systems via block pulse functions
cites work: Solution of integral equations via Laguerre polynomials
cites work: Direct approach for the optimal control of linear time-delay systems via shifted Legend re polynomials
cites work: Solution of linear two-point boundary value problems and optimal control of time-varying systems by shifted Chebyshev approximations
cites work: Solutions of convolution integral and Fredholm integral equations via double Fourier series
cites work: Identification of non-linear distributed system using Walsh functions†
cites work: Identification of non-linear distributed systems via block-pulse functions
cites work: Parameter identification of non-linear systems using Laguerre operational matrices
cites work: Parameter identification of non-linear systems via shifted Chebyshev series
cites work: Legendre series for the identification of non-linear lumped systems
cites work: The Fourier series operational matrix of integration
full work available at URL: 0096-3003(94)00093-j
OpenAlex ID: W2029577600
description: scientific article; zbMATH DE number 753903