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Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations
期刊论文
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 卷号: 400, 页码: 17
作者:
Guo, Ling
;
Wu, Hao
;
Yu, Xiaochen
;
Zhou, Tao
收藏
  |  
浏览/下载:10/0
  |  
提交时间:2023/02/07
Physics -informed neural networks
Fractional Laplacian
Nonlocal operators
Uncertainty quantification
Fast Compact Difference Scheme for Solving the Two-Dimensional Time-Fractional Cattaneo Equation
期刊论文
FRACTAL AND FRACTIONAL, 2022, 卷号: 6, 期号: 8
作者:
Nong, Lijuan
;
Yi, Qian
;
Cao, Jianxiong
;
Chen, An
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  |  
浏览/下载:16/0
  |  
提交时间:2022/09/22
time-fractional Cattaneo equation
compact difference operator
L2-1(sigma) method
fast discrete Sine transform
sum of exponentials
The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation
期刊论文
NUMERICAL ALGORITHMS, 2021, 卷号: 87, 期号: 3, 页码: 1229-1255
作者:
Yang, Fan
;
Pu, Qu
;
Li, Xiao-Xiao
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  |  
浏览/下载:6/0
  |  
提交时间:2021/10/14
Time-fractional diffusion equation
Fractional Laplacian
Identifying the unknown source
Fractional Landweber regularization
Ill-posed problem
Error estimates for a robust finite element method of two-term time-fractional diffusion-wave equation with nonsmooth data
期刊论文
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2021, 卷号: 16
作者:
Nong, Lijuan
;
Chen, An
;
Cao, Jianxiong
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  |  
浏览/下载:10/0
  |  
提交时间:2021/04/12
Two-term time-fractional diffusion-wave equation
finite element method
convolution quadrature
error estimate
Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method
期刊论文
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2021, 卷号: 29, 期号: 12, 页码: 2040-2084
作者:
Yang, Fan
;
Wang, Qian-Chao
;
Li, Xiao-Xiao
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  |  
浏览/下载:12/0
  |  
提交时间:2021/06/03
Inverse problem
Caputo-Fabrizio fractional derivative
space-time fractional diffusion equation
optimal error bound
unknown source identification
Space-time finite element method for the distributed-order time fractional reaction diffusion equations
期刊论文
APPLIED NUMERICAL MATHEMATICS, 2020, 卷号: 152, 页码: 446-465
作者:
Bu, Weiping
;
Ji, Lun
;
Tang, Yifa
;
Zhou, Jie
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  |  
浏览/下载:16/0
  |  
提交时间:2020/05/24
Distributed-order reaction diffusion equation
Space-time finite element method
Graded time mesh
Well-posedness
Error estimate
Sum-of-exponentials approximation
The Quasi-Boundary Value Method for Identifying the Initial Value of the Space-Time Fractional Diffusion Equation
期刊论文
ACTA MATHEMATICA SCIENTIA, 2020, 卷号: 40, 期号: 3, 页码: 641-658
作者:
Yang, Fan
;
Zhang, Yan
;
Liu, Xiao
;
Li, Xiaoxiao
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  |  
浏览/下载:5/0
  |  
提交时间:2022/03/01
Space-time fractional diffusion equation
Ill-posed problem
quasi-boundary value method
identifying the initial value
Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation
期刊论文
NUMERICAL ALGORITHMS, 2020, 卷号: 83, 期号: 4, 页码: 1509-1530
作者:
Yang, Fan
;
Zhang, Yan
;
Li, Xiao-Xiao
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  |  
浏览/下载:7/0
  |  
提交时间:2020/06/02
Initial value problem
Time-space fractional diffusion-wave equation
Landweber iterative regularization method
Error estimate
Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain
期刊论文
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 卷号: 2020, 期号: 1
作者:
Yang, Fan
;
Zhang, Pan
;
Li, Xiao-Xiao
;
Ma, Xin-Yi
收藏
  |  
浏览/下载:5/0
  |  
提交时间:2020/06/02
Time-fractional diffusion equation
Ill-posed problem
Regularization method
Error estimate
A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time–space fractional diffusion equation
期刊论文
Journal of Computational and Applied Mathematics, 2019, 卷号: 362, 页码: 99-115
作者:
Zhao, Yong-Liang
;
Zhu, Pei-Yong
;
Gu, Xian-Ming
;
Zhao, Xi-Le
;
Cao, Jianxiong
收藏
  |  
浏览/下载:5/0
  |  
提交时间:2020/11/14
Gradient methods
Linear systems
Matrix algebra
Partial differential equations
Circulant preconditioner
Fractional differential equations
Krylov subspace method
Toeplitz matrices
WSGD
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