Crank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation

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dc.contributor.authorChen, Wenping
dc.contributor.authorLu, Shujuan
dc.contributor.authorChen, Hu
dc.contributor.authorLiu, Haiyu
dc.date.accessioned2021-11-29T16:47:44Z
dc.date.available2021-11-29T16:47:44Z
dc.date.issued2019-05-31
dc.description.abstractIn this article, we consider spectral methods for solving the initial-boundary value problem of the space fractional-order Allen-Cahn equation. A fully discrete scheme based on the modified Crank-Nicolson scheme in time and the Legendre spectral method in space is established. The existence and uniqueness of the fully discrete scheme are derived, and the stability and convergence analysis of the fully discrete scheme are proved rigorously. By constructing a fractional duality argument, the corresponding optimal error estimates in L2 and Hα norm are derived, respectively. Also, numerical experiments are performed to support the theoretical results.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationChen, W., Lu, S., Chen, H., & Liu, H. (2019). Crank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation. Electronic Journal of Differential Equations, 2019(76), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14964
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSpace-fractional Allen-Cahn equation
dc.subjectLegendre spectral method
dc.subjectModified Crank-Nicolson scheme
dc.subjectStability
dc.subjectConvergence
dc.titleCrank-Nicolson Legendre spectral approximation for space-fractional Allen-Cahn equation
dc.typeArticle

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