Wavelet-based collocation methods for solving multi-dimensional integro-differential systems

Abbas Mohsin Kazar ()

Edelweiss Applied Science and Technology, 2024, vol. 8, issue 6, 4599-4610

Abstract: This paper presents a comprehensive investigation of wavelet-based collocation methods for solving multi-dimensional integro-differential systems. The research addresses the challenging problem of finding numerical solutions to integro-differential equations (IDEs) that are essential in various scientific and engineering applications. We propose novel numerical approximations for infinitely dimensional problems, including fractional Cattaneo-Rayleigh waves and nonlinear diffusion problems defined on unbounded domains. The study introduces a unified computational strategy that directly applies to IDEs without discretization, particularly focusing on the integer and fractional-order Cattaneo-Rayleigh model of thermoelasticity in one-dimensional zonal regions. Through numerical experiments, we demonstrate that our wavelet collocation approach achieves high efficiency and superior accuracy compared to traditional methods. The results show particularly strong performance in handling systems with differential physical singularities, functional physical singularities, and vector-valued physical singularities. Our approach provides a valuable toolbox for addressing complex modeling challenges in biology, mechanical signal processing, and digital communications where partial integro-differential equations naturally arise.

Keywords: integro-differential equations; integro-differential systems; multi-dimensional; Wavelet-based collocation. (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://learning-gate.com/index.php/2576-8484/article/view/2990/1127 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ajp:edwast:v:8:y:2024:i:6:p:4599-4610:id:2990

Access Statistics for this article

More articles in Edelweiss Applied Science and Technology from Learning Gate
Bibliographic data for series maintained by Melissa Fernandes ().