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
收藏
页码：10 / 21
页数：12
相关论文
共 24 条
  • [11] El-Shahed M, 2017, TWMS J PURE APPL MAT, V8, P83
  • [12] A numerical method for the fractional Schrodinger type equation of spatial dimension two
    Ford, Neville J.
    Manuela Rodrigues, M.
    Vieira, Nelson
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (02) : 454 - 468
  • [13] Khan N. A., 2012, Int. Sch. Res. Not, V2012, P1, DOI [10.5402/2012/197068, DOI 10.5402/2012/197068]
  • [14] Fractional quantum mechanics
    Laskin, N
    [J]. PHYSICAL REVIEW E, 2000, 62 (03) : 3135 - 3145
  • [15] Mahmudov N, 2017, TWMS J PURE APPL MAT, V8, P160
  • [16] A Fractional Schrodinger Equation and Its Solution
    Muslih, Sami I.
    Agrawal, Om P.
    Baleanu, Dumitru
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2010, 49 (08) : 1746 - 1752
  • [17] Time fractional Schrodinger equation
    Naber, M
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2004, 45 (08) : 3339 - 3352
  • [18] Odibat Z., 2008, J PHYS C SERIES, V96, P1
  • [19] On the solution of the fractional nonlinear Schrodinger equation
    Rida, S. Z.
    EI-Sherbiny, H. M.
    Arafa, A. A. M.
    [J]. PHYSICS LETTERS A, 2008, 372 (05) : 553 - 558
  • [20] Computational solution of a fractional generalization of the Schrodinger equation occurring in quantum mechanics
    Saxena, R. K.
    Saxena, Ravi
    Kalla, S. L.
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (05) : 1412 - 1417
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