A Family of Transformed Difference Schemes for Nonlinear Time-Fractional Equations

被引：3
|
作者：
Qin, Hongyu [1 ]
Chen, Xiaoli [2 ,3 ]
Zhou, Boya [4 ]
机构：
[1] Wuhan Inst Technol, Sch Math & Phys, Wuhan 430205, Peoples R China
[2] Natl Univ Singapore, Inst Funct Intelligent Mat, Singapore 117544, Singapore
[3] Natl Univ Singapore, Dept Math, Singapore 119077, Singapore
[4] Foshan Univ, Sch Math & Big Data, Foshan 528000, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 01期
基金：
中国国家自然科学基金;
关键词：
time-fractional parabolic problems; change in variable; convergence; optimal error estimates; linearized schemes; CONVOLUTION QUADRATURE; NUMERICAL-METHODS;
D O I：
10.3390/fractalfract7010096
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we present a class of finite difference methods for numerically solving fractional differential equations. Such numerical schemes are developed based on the change in variable and piecewise interpolations. Error analysis of the numerical schemes is obtained by using a Gronwall-type inequality. Numerical examples are given to confirm the theoretical results.
引用
收藏
页数：11
相关论文
共 50 条
  • [31] A fast linearized numerical method for nonlinear time-fractional diffusion equations
    Lyu, Pin
    Vong, Seakweng
    NUMERICAL ALGORITHMS, 2021, 87 (01) : 381 - 408
  • [32] On a new technique for solving the nonlinear conformable time-fractional differential equations
    Hosseini, K.
    Bekir, A.
    Kaplan, M.
    Guner, O.
    OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (11)
  • [33] A fast linearized numerical method for nonlinear time-fractional diffusion equations
    Pin Lyu
    Seakweng Vong
    Numerical Algorithms, 2021, 87 : 381 - 408
  • [34] Solitary Wave Solutions of Nonlinear Conformable Time-Fractional Boussinesq Equations
    Guner, O.
    Bekir, A.
    Hosseini, K.
    ACTA PHYSICA POLONICA A, 2019, 136 (01) : 135 - 140
  • [35] On a new technique for solving the nonlinear conformable time-fractional differential equations
    K. Hosseini
    A. Bekir
    M. Kaplan
    Ö. Güner
    Optical and Quantum Electronics, 2017, 49
  • [36] A novel approach for the analytical solution of nonlinear time-fractional differential equations
    Zhang, Haiyan
    Nadeem, Muhammad
    Rauf, Asim
    Guo Hui, Zhao
    INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2021, 31 (04) : 1069 - 1084
  • [37] On a new technique for solving the nonlinear conformable time-fractional differential equations
    Hosseini, K.
    Bekir, A.
    Kaplan, M.
    Güner, Ö.
    Optical and Quantum Electronics, 2017, 49 (11):
  • [38] Nonlinear stochastic time-fractional slow and fast diffusion equations on Rd
    Chen, Le
    Hu, Yaozhong
    Nualart, David
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (12) : 5073 - 5112
  • [39] The characteristic difference DDM for solving the time-fractional order convection–diffusion equations
    Zhongguo Zhou
    Ning Wang
    Hao Pan
    Yan Wang
    Computational and Applied Mathematics, 2023, 42
  • [40] A fast difference scheme for the variable coefficient time-fractional diffusion wave equations
    Ran, Maohua
    Lei, Xiaojuan
    APPLIED NUMERICAL MATHEMATICS, 2021, 167 : 31 - 44
12345