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

共 50 条

[31] A NEW NND DIFFERENCE SCHEME OF SECOND-ORDER IN TIME AND SPACE
吴望一
蔡庆东
AppliedMathematicsandMechanics(EnglishEdition), 2000, (06) : 617 - 630
[32] A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative
Liu, Zhengguang
Cheng, Aijie
Li, Xiaoli
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (02) : 396 - 411
[33] A second-order BDF compact difference scheme for fractional-order Volterra equation
Chen, Hongbin
Gan, Siqing
Xu, Da
Liu, Qiwen
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2016, 93 (07) : 1140 - 1154
[34] Linearized Crank-Nicolson scheme for the nonlinear time-space fractional Schrodinger equations
Ran, Maohua
Zhang, Chengjian
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 355 : 218 - 231
[35] DETERMINATION OF RECURRENT TIME-SPACE OF SECOND-ORDER
MCLENAGH.RG
THOMPSON, AH
BULLETIN DE LA CLASSE DES SCIENCES ACADEMIE ROYALE DE BELGIQUE, 1972, 58 (09): : 1099 - 1111
[36] Implicit Difference Scheme of the Space-Time Fractional Advection Diffusion Equation
E. A. Abdel-Rehim
Fractional Calculus and Applied Analysis, 2015, 18 : 1452 - 1469
[37] IMPLICIT DIFFERENCE SCHEME OF THE SPACE-TIME FRACTIONAL ADVECTION DIFFUSION EQUATION
Abdel-Rehim, E. A.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2015, 18 (06) : 1452 - 1469
[38] A fourth-order difference scheme for the fractional nonlinear Schrodinger equation with wave operator
Pan, Kejia
Zeng, Jiali
He, Dongdong
Zhang, Saiyan
APPLICABLE ANALYSIS, 2022, 101 (08) : 2886 - 2902
[39] A Second-Order Scheme for the Generalized Time-Fractional Burgers' Equation
Chawla, Reetika
Kumar, Devendra
Singh, Satpal
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2024, 19 (01):
[40] IMPLICIT SCHEME OF THE FINITE DIFFERENCE METHOD FOR THE SECOND-ORDER DUAL PHASE LAG EQUATION
Majchrzak, Ewa
Mochnacki, Bohdan
JOURNAL OF THEORETICAL AND APPLIED MECHANICS, 2018, 56 (02) : 393 - 402

← 1 2 3 4 5 →