Wavelets collocation method for singularly perturbed differential–difference equations arising in control system
Loading...
Date
2023-12
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this paper, we present a wavelet collocation method for efficiently solving singularly
perturbed differential–difference equations (SPDDEs) and one-parameter singularly perturbed
differential equations (SPDEs) taking into account the singular perturbations inherent in control
systems. These equations represent a class of mathematical models that exhibit a combination
of differential and difference equations, making their analysis and solution challenging. The
terms that include negative and positive shifts were approximated using Taylor series expansion.
The main aim of this technique is to convert the problems by using operational matrices of
integration of Haar wavelets into a system of algebraic equations that can be solved using
Newton’s method. The adaptability and multi-resolution properties of wavelet functions offer
the ability to capture system behavior across various scales, effectively handling singular
perturbations present in the equations. Numerical experiments were conducted to showcase
the effectiveness and accuracy of the wavelet collocation method, demonstrating its potential
as a reliable tool for analyzing and solving SPDDEs in control system.