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DC Field | Value | Language |
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dc.citation.startPage | 125228 | - |
dc.citation.title | APPLIED MATHEMATICS AND COMPUTATION | - |
dc.citation.volume | 379 | - |
dc.contributor.author | Kim, Hyunju | - |
dc.contributor.author | Kim, Keon Ho | - |
dc.contributor.author | Lee, Seyeon | - |
dc.contributor.author | Jang, Bongsoo | - |
dc.date.accessioned | 2023-12-21T17:12:02Z | - |
dc.date.available | 2023-12-21T17:12:02Z | - |
dc.date.created | 2020-04-17 | - |
dc.date.issued | 2020-08 | - |
dc.description.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 < nu < 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 v for linear and quadratic interpolations, which are O(h(2-nu)) and O(h(3-nu)) respectively. In order to overcome a strong singular issue as nu approximate to 0 we propose the explicit predictor-corrector scheme with perturbation technique. In case of nu approximate to 1, the truncation errors are reduced by O(h) and O(h(2)). In order to accelerate the con- vergence rate, we decompose nu = nu/2 + nu/2, 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. (C) 2020 Elsevier Inc. All rights reserved. | - |
dc.identifier.bibliographicCitation | APPLIED MATHEMATICS AND COMPUTATION , v.379, pp.125228 | - |
dc.identifier.doi | 10.1016/j.amc.2020.125228 | - |
dc.identifier.issn | 0096-3003 | - |
dc.identifier.scopusid | 2-s2.0-85083028856 | - |
dc.identifier.uri | https://scholarworks.unist.ac.kr/handle/201301/31977 | - |
dc.identifier.url | https://www.sciencedirect.com/science/article/pii/S0096300320301971 | - |
dc.identifier.wosid | 000531501900001 | - |
dc.language | 영어 | - |
dc.publisher | ELSEVIER SCIENCE INC | - |
dc.title | New explicit and accelerated techniques for solving fractional order differential equations | - |
dc.type | Article | - |
dc.description.isOpenAccess | FALSE | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.type.docType | Article | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Caputo fractional derivative | - |
dc.subject.keywordAuthor | Fractional differential equations | - |
dc.subject.keywordAuthor | Predictor-corrector methods | - |
dc.subject.keywordAuthor | Explicit scheme | - |
dc.subject.keywordAuthor | High-order method | - |
dc.subject.keywordPlus | NUMERICAL-SOLUTION | - |
dc.subject.keywordPlus | APPROXIMATION | - |
dc.subject.keywordPlus | SCHEME | - |
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