Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

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....

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Bibliographic Details
Published inOptimal control applications & methods Vol. 41; no. 2; pp. 395 - 416
Main Authors Sabermahani, Sedigheh, Ordokhani, Yadollah, Yousefi, Sohrab‐Ali
Format Journal Article
LanguageEnglish
Published Glasgow Wiley Subscription Services, Inc 01.03.2020
Subjects
Delay
Fibonacci wavelets
Galerkin method
Initial conditions
Iterative methods
Numerical methods
numerical solution
operational matrix
Optimal control
time‐varying delay problem
Wavelet analysis
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Summary: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.
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content type line 14
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.2549