Affiliation:
1. CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Abstract
Abstract
The Grünwald–Letnikov approximation is a well-known discretization to approximate a Riemann–Liouville derivative of order $\alpha>0$. This approximation has been proved to be a consistent approximation, of order $1 $, when the domain is the real line, using Fourier transforms. However, in recent years, this approximation has been applied frequently to solve fractional differential equations in bounded domains and the result proved for the real line has been assumed to be true in general. In this work we show that when assuming a bounded domain, the Grünwald–Letnikov approximation can be inconsistent, for a large number of cases, and when it is consistent we have mostly an order of $n-\alpha $, for $n-1<\alpha <n$.
Funder
Centre for Mathematics of the University of Coimbra
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献