Finite element method for time-space-fractional Schrodinger equation

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dc.contributor.authorZhu, Xiaogang
dc.contributor.authorYuan, Zhanbin
dc.contributor.authorWang, Jungang
dc.contributor.authorNie, Yufeng
dc.contributor.authorYang, Zongze
dc.date.accessioned2022-06-06T18:49:12Z
dc.date.available2022-06-06T18:49:12Z
dc.date.issued2017-07-05
dc.description.abstractIn this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS) with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
dc.description.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationZhu, X., Yuan, Z., Wang, J., Nie, Y., & Yang, Z. (2017). Finite element method for time-space-fractional Schrodinger equation. Electronic Journal of Differential Equations, 2017(166), pp. 1-18.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15859
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, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectTime-space-fractional NLS
dc.subjectFinite element method
dc.subjectConvergence
dc.titleFinite element method for time-space-fractional Schrodinger equation
dc.typeArticle

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