Finite element method for time-space-fractional Schrodinger equation
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Date
2017-07-05
Authors
Zhu, Xiaogang
Yuan, Zhanbin
Wang, Jungang
Nie, Yufeng
Yang, Zongze
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Time-space-fractional NLS, Finite element method, Convergence
Citation
Zhu, 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.
Rights
Attribution 4.0 International