The global analysis on the spectral collocation method for time fractional Schrödinger equation

Minling Zheng, Fawang Liu and Zhengmeng Jin

Applied Mathematics and Computation, 2020, vol. 365, issue C

Abstract: In this paper, a spectral collocation method is proposed and analyzed for solving the time fractional Schrödinger equation. The space derivative is discretized using the collocation method and the time fractional derivative using Grünwald–Letnikov formulation. The stability and convergence of the full discretization scheme are analyzed based on the z-transform. The global behavior of the finite difference spectral collocation method is derived. Numerical examples show a good agreement with the theoretical analysis.

Keywords: Time fractional Schrödinger equation; Caputo fractional derivative; z-transform; Spectral collocation method (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:365:y:2020:i:c:s0096300319306812

DOI: 10.1016/j.amc.2019.124689

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