A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel
type: Item
instance of: scholarly article
title: A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel
author: Yanyan Li
published in: Applied Numerical Mathematics
publication date: 2022-12-09T00:00:00Z
review text: The paper focuses on the numerical solution of fourth-order time-fractional integro-differential equations defined on a rectangular domain and containing an integral operator with a weakly singular kernel. First, scaling functions are defined as Gegenbauer orthogonal polynomials, and the Riemann-Lieuville fractional integral operator for these scaling functions is expressed using the Laplace transform. Then, the authors use a collocation method with the Gegenbauer scaling functions and uniformly distributed collocation points to convert the problem into a system of linear algebraic equations. Furthermore, the authors establish error estimates for the operators involved and the truncation error estimate. Numerical experiments are presented to confirm the theoretical results.
reviewed by: Dana Černá
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 35R09
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7630330
zbMATH Keywords: collocation method
zbMATH Keywords: wavelet
zbMATH Keywords: Gegenbauer polynomials
zbMATH Keywords: integro-differential equations
zbMATH Keywords: fractional derivative
zbMATH Keywords: error estimates
describes a project that uses: FODE
MaRDI profile type: Publication
full work available at URL: j.apnum.2022.10.003
OpenAlex ID: W4306709696
Wikidata QID: Q115360223
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DOI: 10.1016/J.APNUM.2022.10.003
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description: scientific article; zbMATH DE number 7630330