Thumbnail Image
Publication

A fractional Adams method for Caputo fractional differential equations with modified graded meshes

Yang, Yuhui
; 
Yan, Yubin
Advisors
Editors
Other Contributors
Affiliation
Lyuliang University; University of Chester
EPub Date
Publication Date
2025-03-06
Submitted Date
Collections
Mathematics
Show all metadata
Files
Thumbnail Image
Article - VoR
Adobe PDF, 592.36 KB
Other Titles
Abstract
In this paper, we introduce an Adams-type predictor–corrector method based on a modified graded mesh for solving Caputo fractional differential equations. This method not only effectively handles the weak singularity near the initial point but also reduces errors associated with large intervals in traditional graded meshes. We prove the error estimates in detail for both 0<α<1 and 1<α<2 cases, where α is the order of the Caputo fractional derivative. Numerical experiments confirm the convergence of the proposed method and compare its performance with the traditional graded mesh approach.
Citation
Yang, Y., & Yan, Y. (2025). A fractional Adams method for Caputo fractional differential equations with modified graded meshes. Mathematics, 13(5), article-number 891. https://doi.org/10.3390/math13050891
Publisher
MDPI
Journal
Mathematics
Research Unit
URI
http://hdl.handle.net/10034/629302
DOI
10.3390/math13050891
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Series/Report no.
ISSN
EISSN
2227-7390
ISBN
ISMN
Gov't Doc
Test Link
Sponsors
Unfunded
Additional Links
https://www.mdpi.com/2227-7390/13/5/891