Numerical Analysis of the Nonuniform Fast L1 Formula for Nonlinear Time-Space Fractional Parabolic Equations

被引：5
|
作者：
Xing, Zhiyong [1 ]
Wen, Liping [2 ]
机构：
[1] Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China
[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2023年 / 95卷 / 02期
关键词：
Nonlinear time-space fractional parabolic equation; Fast L1 formula; Energy dissipation law; Weak singularity; Stability and convergence; FINITE-DIFFERENCE METHOD; GRADED MESHES; ALLEN-CAHN; SCHEME; STEPS;
D O I：
10.1007/s10915-023-02186-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Basing on the nonuniform fast L1 formula, an efficient numerical scheme is proposed for nonlinear time-space fractional parabolic equations. The stability and convergence of the numerical scheme are rigorously established. The discrete energy dissipation property of the numerical scheme based on graded temporal mesh is given. Finally, several numerical experiments are provided to verify the theoretical results.
引用
收藏
页数：22
相关论文
共 50 条
  • [41] Nonuniform Alikhanov Linearized Galerkin Finite Element Methods for Nonlinear Time-Fractional Parabolic Equations
    Boya Zhou
    Xiaoli Chen
    Dongfang Li
    Journal of Scientific Computing, 2020, 85
  • [42] NUMERICAL ANALYSIS FOR STOCHASTIC TIME-SPACE FRACTIONAL DIFFUSION EQUATION DRIVEN BY FRACTIONAL GAUSSIAN NOISE
    Nie, Daxin
    Deng, Weihua
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2023,
  • [43] Numerical analysis for Klein-Gordon equation with time-space fractional derivatives
    Zhang, Jun
    Wang, JinRong
    Zhou, Yong
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (06) : 3689 - 3700
  • [44] SHARP ERROR ESTIMATE OF THE NONUNIFORM L1 FORMULA FOR LINEAR REACTION-SUBDIFFUSION EQUATIONS
    Liao, Hong-Lin
    Li, Dongfang
    Zhang, Jiwei
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (02) : 1112 - 1133
  • [45] Existence and uniqueness result for a class of nonlinear parabolic equations with L1 data
    Redwane, Hicham
    RECENT DEVELOPMENTS IN NONLINEAR ANALYSIS, 2010, : 150 - 169
  • [46] NONLINEAR ANISOTROPIC ELLIPTIC AND PARABOLIC EQUATIONS WITH VARIABLE EXPONENTS AND L1 DATA
    Bendahmane, Mostafa
    Karlsen, Kenneth H.
    Saad, Mazen
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (03) : 1201 - 1220
  • [47] A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
    Huang, Jianfei
    Zhang, Jingna
    Arshad, Sadia
    Tang, Yifa
    APPLIED NUMERICAL MATHEMATICS, 2021, 159 : 159 - 173
  • [48] EFFICIENT NUMERICAL SOLUTION OF TWO-DIMENSIONAL TIME-SPACE FRACTIONAL NONLINEAR DIFFUSION-WAVE EQUATIONS WITH INITIAL SINGULARITY
    Elmahdi, Emadidin Gahalla Mohmed
    Huang, Jianfei
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2022, 12 (02): : 831 - 849
  • [49] Time-space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation
    Tu, Tongbi
    Ercan, Ali
    Kavvas, M. Levent
    HYDROLOGICAL PROCESSES, 2018, 32 (10) : 1406 - 1419
  • [50] Numerical solution of multidimensional time-space fractional differential equations of distributed order with Riesz derivative
    Ghuraibawi, Amer Abdulhussein Mohammed
    Marasi, H. R.
    Derakhshan, M. H.
    Kumar, Pushpendra
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (14) : 15186 - 15207
12345