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

Sabermahani, Sedigheh; Ordokhani, Yadollah; Yousefi, Sohrab‐Ali

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.

NEWTON-Raphson method; WAVELETS (Mathematics); TIME-varying systems; OPTIMAL control theory

Optimal Control - Applications & Methods, 2020, Vol 41, Issue 2, p395

0143-2087

Academic Journal

10.1002/oca.2549