New explicit and accelerated techniques for solving fractional order differential equations

Cited 0 times inthomson ciCited 0 times inthomson ci
Title
New explicit and accelerated techniques for solving fractional order differential equations
Author
Kim, HyunjuKim, Keon HoLee, SeyeonJang, Bongsoo
Issue Date
2020-08
Publisher
Elsevier BV
Citation
APPLIED MATHEMATICS AND COMPUTATION , v.379, no.125228, pp.125228
Abstract
This paper proposes new direct and acceleration numerical methods for solving Fractional order Differential Equations (FDEs). For the Caputo differential operator with fractional order 0 < ν < 1, we rewrite the FDE as an equivalent integral form circumventing the derivative of the solution by the integral by parts. We obtain a discrete formulation directly from the integral form using the Lagrange interpolate polynomials. We provide truncation errors depending on the fractional order ν for linear and quadratic interpolations, which are and respectively. In order to overcome a strong singular issue as ν ≈ 0 we propose the explicit predictor-corrector scheme with perturbation technique. In case of ν ≈ 1, the truncation errors are reduced by and . In order to accelerate the convergence rate, we decompose convert the FDE into the system of FDEs, and apply the predictor-corrector scheme. Numerical tests for linear, nonlinear, variable order and time-fractional sub-diffusion problems demonstrate that the proposed methods give a prominent performance. We also compare the numerical results with other high-order explicit and implicit schema.
URI
https://scholarworks.unist.ac.kr/handle/201301/31977
URL
https://www.sciencedirect.com/science/article/pii/S0096300320301971
DOI
10.1016/j.amc.2020.125228
ISSN
0096-3003
Appears in Collections:
SNS_Journal Papers
Files in This Item:
There are no files associated with this item.

find_unist can give you direct access to the published full text of this article. (UNISTARs only)

Show full item record

qrcode

  • mendeley

    citeulike

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

MENU