A second-order implicit difference scheme for the nonlinear time-space fractional Schrodinger equation

被引：13

作者：

Fei, Mingfa ^{[1
,2
]}

Wang, Nan ^{[3
]}

Huang, Chengming ^{[4
]}

Ma, Xiaohua ^{[5
]}

机构：

[1] Changsha Univ, Sch Comp Engn & Appl Math, Changsha 410022, Peoples R China

[2] Changsha Univ, Hunan Prov Key Lab Ind Internet Technol & Secur, Changsha 410022, Peoples R China

[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

[4] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[5] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410022, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 153卷

基金：

中国博士后科学基金;

关键词：

Time-space fractional Schrodinger equation; Caputo derivative; Riesz fractional derivative; L2-1(sigma) formula; Convergence; Unique solvability; FINITE-ELEMENT-METHOD; SPECTRAL METHOD; WELL-POSEDNESS;

D O I：

10.1016/j.apnum.2020.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop an implicit difference method for solving the nonlinear time-space fractional Schrodinger equation. The scheme is constructed by using the L2-1(sigma) formula to approximate the Caputo fractional derivative, while the weighted and shifted Grunwald formula is adopted for the spatial discretization. The stability and unique solvability of the difference scheme are analyzed in detail. Moreover, we prove that the numerical solution is convergent with second-order accuracy in both temporal and spatial directions. Finally, a linearized iterative algorithm is provided and some numerical tests are presented to validate our theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：399 / 411

页数：13

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