Stability of difference schemes for fractional equations
type: Item
instance of: scholarly article
title: Stability of difference schemes for fractional equations
zbMATH Open document ID: 1329.65166
DOI: 10.1134/S0012266115070095
author: Ru Liu
author: Miao Li
author: S. I. Piskarev
published in: Differential Equations
publication date: 2015-10-14T00:00:00Z
review text: The authors studies the stability of the approximate schemes for the Cauchy problem with the fractional derivative \[ (D^{\alpha}_{t} u)(t)= A u(t), \qquad u(0)= x, \qquad 0< \alpha \leq 1, \] in the Banach space. The approximate schemes are constructed using the explicit and implicit finite difference formulas. The proof of the stability is based on the known theorem of Trotter-Kato.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 65J08
zbMATH DE Number: 6493789
zbMATH Keywords: Cauchy problem with the fractional derivative
zbMATH Keywords: finite difference schemes
zbMATH Keywords: stability
zbMATH Keywords: Banach space
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
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full work available at URL: s0012266115070095
OpenAlex ID: W1900148221
description: scientific article; zbMATH DE number 6493789