Difference Approximation for 2D Time-Fractional Integro-Differential Equation with Given Initial and Boundary Conditions

被引：0
|
作者：
Zhang, Xindong [1 ]
Luo, Ziyang [2 ]
Tang, Quan [3 ]
Wei, Leilei [4 ]
Liu, Juan [1 ]
机构：
[1] Guizhou Univ Finance & Econ, Coll Big Data Stat, Guiyang 550025, Peoples R China
[2] Xinjiang Inst Engn, Sch Math & Phys, Urumqi 830023, Peoples R China
[3] Xinjiang Normal Univ, Sch Math Sci, Urumqi 830017, Peoples R China
[4] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China
来源：
FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 08期
关键词：
integro-differential equation; Riemann-Liouville derivative; compact finite difference method; stability; convergence; ERROR ANALYSIS; SCHEME; DIFFUSION; ADI; CONDUCTION; SPACE;
D O I：
10.3390/fractalfract8080495
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this investigation, a new algorithm based on the compact difference method is proposed. The purpose of this investigation is to solve the 2D time-fractional integro-differential equation. The Riemann-Liouville derivative was utilized to define the time-fractional derivative. Meanwhile, the weighted and shifted Gr & uuml;nwald difference operator and product trapezoidal formula were utilized to construct a high-order numerical scheme. Also, we analyzed the stability and convergence. The convergence order was O(tau 2+hx4+hy4), where tau is the time step size, hx and hy are the spatial step sizes. Furthermore, several examples were provided to verify the correctness of our theoretical reasoning.
引用
收藏
页数：17
相关论文
共 50 条
  • [31] Approximation of Solutions to Stochastic Fractional Integro-Differential Equation with Deviated Argument
    Chaudhary, Renu
    Pandey, Dwijendra N.
    DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2020, 28 (02) : 337 - 356
  • [32] Approximation of Solutions to Stochastic Fractional Integro-Differential Equation with Deviated Argument
    Renu Chaudhary
    Dwijendra N. Pandey
    Differential Equations and Dynamical Systems, 2020, 28 : 337 - 356
  • [33] An efficient spline technique for solving time-fractional integro-differential equations
    Abbas, Muhammad
    Aslam, Sadia
    Abdullah, Farah Aini
    Riaz, Muhammad Bilal
    Gepreel, Khaled A.
    HELIYON, 2023, 9 (09)
  • [34] Existence, Uniqueness and Approximation of Solution for the Fractional Semilinear Integro-differential Equation
    Chadha, Alka
    Pandey, D. N.
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2014, 52 (03): : 73 - 89
  • [35] Time-fractional integro-differential equations in power growth function spaces
    Phung Dinh Tran
    Duc Thanh Dinh
    Tuan Kim Vu
    M. Garayev
    H. Guediri
    Fractional Calculus and Applied Analysis, 2023, 26 : 751 - 780
  • [36] Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation
    Jangveladze, Temur
    Kiguradze, Zurab
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2011, 9 (04): : 866 - 873
  • [37] Time-fractional integro-differential equations in power growth function spaces
    Tran, Phung Dinh
    Dinh, Duc Thanh
    Vu, Tuan Kim
    Garayev, M.
    Guediri, H.
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (02) : 751 - 780
  • [38] Existence and stability results for ψ-Hilfer fractional integro-differential equation with mixed nonlocal boundary conditions
    Sudsutad, Weerawat
    Thaiprayoon, Chatthai
    Ntouyas, Sotiris K.
    AIMS MATHEMATICS, 2021, 6 (04): : 4119 - 4141
  • [39] Delay integro-differential inequalities with initial time difference and applications
    Jankowski, T
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 291 (02) : 605 - 624
  • [40] On Fractional Integro-Differential Equation with Nonlinear Time Varying Delay
    Soliman, A. A.
    Raslan, K. R.
    Abdallah, A. M.
    SOUND AND VIBRATION, 2022, 56 (02): : 147 - 163
12345