New numerical solutions of fractional-order Korteweg-de Vries equation

被引：25
|
作者：
Inc, Mustafa [1 ,2 ]
Parto-Haghighi, Mohammad [3 ]
Akinlar, Mehmet Ali [4 ]
Chu, Yu-Ming [5 ,6 ]
机构：
[1] Firat Univ, Dept Math, Elazig, Turkey
[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
[3] Univ Bonab, Dept Math, Bonab, Iran
[4] Yildiz Tech Univ, Dept Engn Math, Istanbul, Turkey
[5] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[6] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China
来源：
RESULTS IN PHYSICS | 2020年 / 19卷
关键词：
Time fractional Korteweg de Vries equation; Fictitious time integration; Group preserving scheme (GPS); Caputo derivative; GROUP PRESERVING SCHEME; KLEIN-GORDON EQUATIONS; GROUP SHOOTING METHOD; DIFFUSION; MODELS;
D O I：
10.1016/j.rinp.2020.103326
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present new solutions of fractional-order Korteweg-de Vries (KdV) equation by employing a method that utilizes advantages of both techniques of fictititous time integration and group preserving. Proposed method converts the KdV to a new system of equations which is approximately solved by a semi-discretization numerical scheme. Caputo type fractional-order derivative operators are used. We apply the method to some specific cases of the KdV equation. Computational results indicate that the method gives new and highly efficient solutions of the KdV equation.
引用
收藏
页数：5
相关论文
共 50 条
  • [1] Numerical Solutions of the Multi-Space Fractional-Order Coupled Korteweg-De Vries Equation with Several Different Kernels
    Saad, Khaled Mohammed
    Srivastava, Hari Mohan
    FRACTAL AND FRACTIONAL, 2023, 7 (10)
  • [2] Numerical Algorithms for Solutions of Korteweg-de Vries Equation
    Korkmaz, Alper
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (06) : 1504 - 1521
  • [3] On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation
    Mendez, Argenis J.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (11) : 9051 - 9089
  • [4] A Novel Approach for Korteweg-de Vries Equation of Fractional Order
    Jassim, Hassan Kamil
    Baleanu, Dumitru
    JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2019, 5 (02): : 192 - 198
  • [5] NUMERICAL SOLUTIONS OF TIME FRACTIONAL KORTEWEG-DE VRIES EQUATION AND ITS STABILITY ANALYSIS
    Yokus, Asif
    COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2019, 68 (01): : 353 - 361
  • [6] APPROXIMATE ANALYTICAL SOLUTIONS OF GENERALIZED FRACTIONAL KORTEWEG-DE VRIES EQUATION
    Deng, Shuxian
    Deng, Zihao
    THERMAL SCIENCE, 2023, 27 (3A): : 1873 - 1879
  • [7] Bright Soliton Solutions for Time Fractional Korteweg-de Vries Equation
    Ozkan, Erdogan Mehmet
    Ozkan, Ayten
    INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 2325
  • [8] ENHANCED EXISTENCE TIME OF SOLUTIONS TO THE FRACTIONAL KORTEWEG-DE VRIES EQUATION
    Ehrnstrom, Mats
    Wang, Yuexun
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (04) : 3298 - 3323
  • [9] On the singular solutions of the Korteweg-de Vries equation
    S. I. Pokhozhaev
    Mathematical Notes, 2010, 88 : 741 - 747
  • [10] Solutions to the modified Korteweg-de Vries equation
    Zhang, Da-Jun
    Zhao, Song-Lin
    Sun, Ying-Ying
    Zhou, Jing
    REVIEWS IN MATHEMATICAL PHYSICS, 2014, 26 (07)
12345