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 |
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