High-Order Approximation to Caputo Derivatives and Caputo-type Advection–Diffusion Equations: Revisited. (3rd July 2017)

• Record Type: Journal Article
• Authors: Li, Changpin; Cai, Min
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 7(2017)
• Page Start: 861
• Page End: 890
• Publication Date: 2017-07-03
• Subjects: Caputo derivative -- Caputo-type advection-diffusion equation -- convergence -- Fourier transform -- high-order approximation; 26A33; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1291521
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, a series of new high-order numerical approximations to α -th Caputo derivatives (0< α <2) is derived based on a compound of shift operators and high-order approximations to Riemann–Liouville derivatives. The convergence order is independent of the derivative order α, rather than the previous error estimates. Several numerical examples including the Caputo-type advection–diffusion equation are displayed, which support the derived numerical schemes.