Please use this identifier to cite or link to this item: http://elar.urfu.ru/handle/10995/118108
Title: High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay
Authors: Amin, A. Z.
Zaky, M. A.
Hendy, A. S.
Hashim, I.
Aldraiweesh, A.
Issue Date: 2022
Publisher: MDPI
Citation: High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay / A. Z. Amin, M. A. Zaky, A. S. Hendy et al. // Mathematics. — 2022. — Vol. 10. — Iss. 17. — 3065.
Abstract: One of the open problems in the numerical analysis of solutions to high-dimensional nonlinear integral equations with memory kernel and proportional delay is how to preserve the high-order accuracy for nonsmooth solutions. It is well-known that the solutions to these equations display a typical weak singularity at the initial time, which causes challenges in developing high-order and efficient numerical algorithms. The key idea of the proposed approach is to adopt a smoothing transformation for the multivariate spectral collocation method to circumvent the curse of singularity at the beginning of time. Therefore, the singularity of the approximate solution can be tailored to that of the exact one, resulting in high-order spectral collocation algorithms. Moreover, we provide a framework for studying the rate of convergence of the proposed algorithm. Finally, we give a numerical test example to show that the approach can preserve the nonsmooth solution to the underlying problems. © 2022 by the authors.
Keywords: MEMORY KERNELS
MULTIDIMENSIONAL INTEGRAL EQUATIONS
NONSMOOTH SOLUTION
SPECTRAL ALGORITHM
URI: http://elar.urfu.ru/handle/10995/118108
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85137798208
WOS ID: 000851855600001
PURE ID: 30897618
ISSN: 22277390
DOI: 10.3390/math10173065
metadata.dc.description.sponsorship: King Saud University, KSU
M. A. Zaky and A. Aldraiweesh extend their appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).
Appears in Collections:Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85137798208.pdf961,16 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.