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Numerical analysis for time-fractional Schrödinger equation on two space dimensions by Jun Zhang; JinRong Wang; Yong Zhou is a Mathematics article available to read on EtoBox.

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## Abstract In this paper, we study the numerical methods for solving the time-fractional Schrödinger equation (TFSE) with Caputo or Riemann–Liouville fractional derivative. The numerical schemes are implemented by using the L1 scheme in time direction and Fourier–Galerkin/Legendre-Galerkin spectral methods in spatial variable. We prove that the two schemes are unconditionally stable and numerical solutions converge with the order $\mathcal{O}( \Delta t^{2-\alpha }+N^{-s}+ N^{-m})$O(Δt2−α+N−s+N−m), where α is the order of the fractional derivative, Δt, N are the step of time and polynomial degree, respectively, m, s are the regularity of u and V. Several numerical results are performed to confirm the theoretical analysis.

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Author

Jun Zhang; JinRong Wang; Yong Zhou

Publisher

Springer International Publishing AG; Springer (Biomed Central Ltd.); Springer Verlag; Cairo: Hindawi; Springer Science and Business Media LLC; Society for Mining, Metallurgy and Exploration Inc. (ISSN 1687-1839)

Published

2020

Language

EN

Field

Mathematics (Physical Sciences)