Zhu, XiaogangYuan, ZhanbinWang, JungangNie, YufengYang, Zongze2022-06-062022-06-062017-07-05Zhu, 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. 1-18.1072-6691https://hdl.handle.net/10877/15859In 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.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalTime-space-fractional NLSFinite element methodConvergenceArticle