| Autor: |
Baoli Yin, Guoyu Zhang, Yang Liu, Hong Li |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Fractal and Fractional, Vol 6, Iss 8, p 417 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2504-3110 |
| DOI: |
10.3390/fractalfract6080417 |
| Popis: |
An exponential-type function was discovered to transform known difference formulas by involving a shifted parameter θ to approximate fractional calculus operators. In contrast to the known θ methods obtained by polynomial-type transformations, our exponential-type θ methods take the advantage of the fact that they have no restrictions in theory on the range of θ such that the resultant scheme is asymptotically stable. As an application to investigate the subdiffusion problem, the second-order fractional backward difference formula is transformed, and correction terms are designed to maintain the optimal second-order accuracy in time. The obtained exponential-type scheme is robust in that it is accurate even for very small α and can naturally resolve the initial singularity provided θ=−12, both of which are demonstrated rigorously. All theoretical results are confirmed by extensive numerical tests. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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