Second-order nonuniform time-stepping schemes for time-fractional evolution equations with general elliptic operator

We extend the numerical methods in Lyu and Vong (2021) to the time-fractional evolution equations with general elliptic operator. By reformulating the mixed derivatives part of the elliptic operator and introducing a different auxiliary multiplicative function, the Alikhanov type schemes are propose...

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Bibliographic Details
Published in:Applied mathematics letters 2023-05, Vol.139, p.108541, Article 108541
Main Authors: Lyu, Pin, Zhou, Linghui, Vong, Seakweng
Format: Article
Language:English
Subjects:
Fractional evolution equation
Mixed derivatives
Nonuniform mesh
Variable coefficients
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Summary:We extend the numerical methods in Lyu and Vong (2021) to the time-fractional evolution equations with general elliptic operator. By reformulating the mixed derivatives part of the elliptic operator and introducing a different auxiliary multiplicative function, the Alikhanov type schemes are proposed for the governing problems on general time meshes. Unconditional stability and second-order convergence are obtained by energy method.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2022.108541