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

机译：斐波纳契小波及其解决两类时变延迟问题的应用

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摘要

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.
机译：在本文中，讨论了解决时变延迟方程的数值方法和与时变延迟系统的最佳控制问题。 该方法基于Fibonacci小波和Petrov-Galerkin方法。 为了解决这些问题，首先，提出了斐波纳契小波。 借助于斐波纳契小波的集成和延迟的运营矩阵，并使用Petrov-Galerkin方法和牛顿的迭代方法，我们在数值上解决了两类时差的延迟问题。 该方法实现的近似解决方案满足所有初始条件。 另外，给出了对错误的估计。 包括数值结果以证明本技术的准确性和适用性。

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