THE NUMERICAL SOLUTION OF THE TIME-FRACTIONAL NON-LINEAR KLEIN-GORDON EQUATION VIA SPECTRAL COLLOCATION METHOD

被引：4
|
作者：
Yang, Yin [1 ]
Yang, Xinfa [2 ]
Wang, Jindi [1 ]
Liu, Jie [3 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Hunan, Peoples R China
[2] Hunan Univ, State Key Lab Adv Design & Mfg Vehicle Body, Changsha, Hunan, Peoples R China
[3] Guangzhou Univ, Sch Mech & Elect Engn, Ctr Res Leading Technol Special Equipment, Guangzhou, Guangdong, Peoples R China
来源：
THERMAL SCIENCE | 2019年 / 23卷 / 03期
关键词：
caputo derivative; non-linear; time fractional Klein-Gordon equation; spectral collocation method; CONVERGENCE;
D O I：
10.2298/TSCI180824220Y
中图分类号：
O414.1 [热力学];
学科分类号：
摘要：
In this paper, we consider the numerical solution of the time fractional non-linear Klein-Gordon equation. We propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. A rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L-2-norm. Numerical tests are carried out to confirm the theoretical results.
引用
收藏
页码：1529 / 1537
页数：9
相关论文
共 50 条
  • [31] THE CAUCHY-PROBLEM FOR THE NON-LINEAR KLEIN-GORDON EQUATION
    GINIBRE, J
    VELO, G
    NEW METHODS AND RESULTS IN NON-LINEAR FIELD EQUATIONS, 1989, 347 : 79 - 90
  • [32] New non-linear modified massless Klein-Gordon equation
    Asenjo, Felipe A.
    Hojman, Sergio A.
    EUROPEAN PHYSICAL JOURNAL C, 2017, 77 (11):
  • [33] A numerical solution of the Klein-Gordon equation and convergence of the decomposition method
    Kaya, D
    El-Sayed, SM
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 156 (02) : 341 - 353
  • [34] Analysis of nonlinear time-fractional Klein-Gordon equation with power law kernel
    Saifullah, Sayed
    Ali, Amir
    Khan, Zareen A.
    AIMS MATHEMATICS, 2022, 7 (04): : 5275 - 5290
  • [35] A collocation method for generalized nonlinear Klein-Gordon equation
    Ben-Yu Guo
    Zhong-Qing Wang
    Advances in Computational Mathematics, 2014, 40 : 377 - 398
  • [36] A collocation method for generalized nonlinear Klein-Gordon equation
    Guo, Ben-Yu
    Wang, Zhong-Qing
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2014, 40 (02) : 377 - 398
  • [37] Analytic Solution of the Fractional Order Non-linear Schrodinger Equation and the Fractional Order Klein Gordon Equation
    Ali, Md Ramjan
    Ghosh, Uttam
    Sarkar, Susmita
    Das, Shantanu
    DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2022, 30 (03) : 499 - 512
  • [38] APPROXIMATE ANALYTICAL SOLUTION OF TIME-FRACTIONAL NON-LINEAR HEAT EQUATION VIA FRACTIONAL POWER SERIES METHOD
    Deng, Shuxian
    Ge, Xinxin
    THERMAL SCIENCE, 2022, 26 (03): : 2637 - 2643
  • [39] Numerical solution of two and three dimensional time fractional damped nonlinear Klein-Gordon equation using ADI spectral element method
    Saffarian, Marziyeh
    Mohebbi, Akbar
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 405
  • [40] A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations
    Taherkhani, Shima
    Najafi, Iraj
    Ghayebi, Bakhtiyar
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2023, 11 (02): : 357 - 368
12345