The Construction of High-Order Robust Theta Methods with Applications in Subdiffusion Models

Autor: Baoli Yin, Guoyu Zhang, Yang Liu, Hong Li
Jazyk: angličtina
Rok vydání: 2022
Předmět:
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
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