Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrödinger equation

Authors:
Leilei Wei;Yinnian He;Xindong Zhang;Shaoli Wang
Affiliations:
Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China;Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China;College of Mathematics Sciences, Xinjiang Normal University, Urumqi 830054, PR China;Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China
Venue:
Finite Elements in Analysis and Design
Year:
2012

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Abstract

In this paper we present and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional Schrodinger equation, where the fractional derivative is described in the Caputo sense. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. A stability and error analysis is performed on the numerical methods. Numerical results confirm the expected convergence rates and illustrate the effectiveness of the method.