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Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems
Author(s) -
Sabermahani Sedigheh,
Ordokhani Yadollah,
Yousefi SohrabAli
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2549
Subject(s) - fibonacci number , wavelet , petrov–galerkin method , fibonacci polynomials , mathematics , galerkin method , computer science , numerical analysis , algorithm , mathematical optimization , mathematical analysis , finite element method , discrete mathematics , artificial intelligence , physics , orthogonal polynomials , difference polynomials , thermodynamics
Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.