dc.citation.number |
1 |
- |
dc.citation.startPage |
65 |
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dc.citation.title |
FRACTAL AND FRACTIONAL |
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dc.citation.volume |
8 |
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dc.contributor.author |
Lee, Seyeon |
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dc.contributor.author |
Kim, Hyunju |
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dc.contributor.author |
Jang, Bongsoo |
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dc.date.accessioned |
2024-01-30T14:05:16Z |
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dc.date.available |
2024-01-30T14:05:16Z |
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dc.date.created |
2024-01-22 |
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dc.date.issued |
2024-01 |
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dc.description.abstract |
In this article, a considerably efficient predictor-corrector method (PCM) for solving Atangana–Baleanu Caputo (ABC) fractional differential equations (FDEs) is introduced. First, we propose a conventional PCM whose computational speed scales with quadratic time complexity 𝒪(𝑁2) as the number of time steps N grows. A fast algorithm to reduce the computational complexity of the memory term is investigated utilizing a sum-of-exponentials (SOEs) approximation. The conventional PCM is equipped with a fast algorithm, and it only requires linear time complexity 𝒪(𝑁) . Truncation and global error analyses are provided, achieving a uniform accuracy order 𝒪(ℎ2) regardless of the fractional order for both the conventional and fast PCMs. We demonstrate numerical examples for nonlinear initial value problems and linear and nonlinear reaction-diffusion fractional-order partial differential equations (FPDEs) to numerically verify the efficiency and error estimates. Finally, the fast PCM is applied to the fractional-order Rössler dynamical system, and the numerical results prove that the computational cost consumed to obtain the bifurcation diagram is significantly reduced using the proposed fast algorithm. |
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dc.identifier.bibliographicCitation |
FRACTAL AND FRACTIONAL, v.8, no.1, pp.65 |
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dc.identifier.doi |
10.3390/fractalfract8010065 |
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dc.identifier.issn |
2504-3110 |
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dc.identifier.uri |
https://scholarworks.unist.ac.kr/handle/201301/74397 |
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dc.language |
영어 |
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dc.publisher |
MDPI AG |
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dc.title |
A Novel Numerical Method for Solving Nonlinear Fractional-Order Differential Equations and Its Applications |
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dc.type |
Article |
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dc.description.isOpenAccess |
TRUE |
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dc.description.journalRegisteredClass |
scie |
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