Error estimates of a spectral Petrov–Galerkin method for two-sided fractional reaction–diffusion equations

Zhaopeng Hao, Guang Lin and Zhongqiang Zhang

Applied Mathematics and Computation, 2020, vol. 374, issue C

Abstract: We study regularity and the spectral method for two-sided fractional diffusion equations with a reaction term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard Sobolev spaces. With this regularity, we prove an optimal error estimate for the spectral Petrov–Galerkin method. Numerical results are presented to verify our theoretical convergence orders.

Keywords: Regularity; Pseudo-eigen functions; Weighted Sobolev spaces; Spectral methods; Optimal error estimates; Riemann–Liouville fractional operators (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032030014X
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:374:y:2020:i:c:s009630032030014x

DOI: 10.1016/j.amc.2020.125045

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().