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

被引：90
|
作者：
Wei, Leilei [1 ]
He, Yinnian [1 ]
Zhang, Xindong [2 ]
Wang, Shaoli [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China
[2] Xinjiang Normal Univ, Coll Math Sci, Urumqi 830054, Peoples R China
来源：
FINITE ELEMENTS IN ANALYSIS AND DESIGN | 2012年 / 59卷
基金：
中国国家自然科学基金;
关键词：
Time-fractional partial differential equations; Schrodinger equation; Local discontinuous Galerkin method; Stability; Error estimates; HOMOTOPY PERTURBATION METHOD; DIFFUSION EQUATION; APPROXIMATION; SPACE;
D O I：
10.1016/j.finel.2012.03.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. Crown Copyright (C) 2012 Published by Elsevier BY. All rights reserved.
引用
收藏
页码：28 / 34
页数：7
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