A STABLE SECOND ORDER OF ACCURACY DIFFERENCE SCHEME FOR A FRACTIONAL SCHRODINGER DIFFERENTIAL EQUATION

被引：0

作者：

Ashyralyev, A. ^{[1
,2
,3
]}

Hicdurmaz, B. ^{[4
]}

机构：

[1] Near East Univ, Dept Math, Mersin 10, Nicosia, Turkey

[2] Peoples Friendship Univ Russia, Ul Miklukho Maklaya 6, Moscow 117198, Russia

[3] Inst Math & Math Modeling, Alma Ata 050010, Kazakhstan

[4] Istanbul Medeniyet Univ, Fac Engn & Nat Sci, Dept Math, TR-34700 Istanbul, Turkey

来源：

APPLIED AND COMPUTATIONAL MATHEMATICS | 2018年 / 17卷 / 01期

关键词：

Stability; Fractional Schrodinger Equation; Difference Scheme; Numerical Results; QUANTUM-MECHANICS; TIME; EXISTENCE; ORDER;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we present and analyze a second order of accuracy difference scheme for solving a fractional Schrodinger differential equation with the fractional derivative in the Riemann Louville sense. A stability analysis is performed on the presented difference scheme. Numerical results confirm the expected convergence rates and illustrate the effectiveness of the method.

引用

页码：10 / 21

页数：12

共 24 条

[1] Ahmad B, 2017, APPL COMPUT MATH-BAK, V16, P148
[2] AMORE P, 2010, J MATH PHYS, V51
[3] [Anonymous], 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0
[4] [Anonymous], 1999, FRACTIONAL DIFFERENT
[5] Nonlocal boundary-value problems for abstract parabolic equations: well-posedness in Bochner spaces
Ashyralyev, A
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2006, 6 (01) : 1 - 28
[6] ASHYRALYEV A, 2014, ELECTRON J DIFF 0721
[7] On the numerical solution of fractional Schrodinger differential equations with the Dirichlet condition
Ashyralyev, Allaberen
Hicdurmaz, Betul
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2012, 89 (13-14) : 1927 - 1936
[8] A note on the fractional Schrodinger differential equations
Ashyralyev, Allaberen
Hicdurmaz, Betul
[J]. KYBERNETES, 2011, 40 (5-6) : 736 - 750
[9] Fractional differential equations and the Schrodinger equation
Ben Adda, F
Cresson, J
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2005, 161 (01) : 323 - 345
[10] Space-time fractional Schrodinger equation with time-independent potentials
Dong, Jianping
Xu, Mingyu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (02) : 1005 - 1017

← 1 2 3 →