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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:11/0
  |  
提交时间:2023/02/07
Physics -informed neural networks
Fractional Laplacian
Nonlocal operators
Uncertainty quantification
Dual-phase-lag thermoelastic diffusion analysis of a size-dependent microplate based on modified fractional-order heat conduction model
期刊论文
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2022
作者:
Tian, Lingchen
;
Peng, Wei
;
He, Tianhu
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  |  
浏览/下载:13/0
  |  
提交时间:2022/09/22
A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition
期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 17
作者:
Zhao, Yue
;
Mao, Zhiping
;
Guo, Ling
;
Tang, Yifa
;
Karniadakis, George Em
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  |  
浏览/下载:11/0
  |  
提交时间:2023/02/07
Uncertainty quantification
Anomalous transport
Quasi Monte Carlo simulation
Generalized polynomial chaos
Long-time integration
Poly-fractonomials
A Superconvergent Nonconforming Mixed FEM for Multi-Term Time-Fractional Mixed Diffusion and Diffusion-Wave Equations with Variable Coefficients
期刊论文
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2021, 卷号: 11, 期号: 1, 页码: 63-92
作者:
Fan, Huijun
;
Zhao, Yanmin
;
Wang, Fenling
;
Shi, Yanhua
;
Tang, Yifa
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  |  
浏览/下载:29/0
  |  
提交时间:2021/01/14
Nonconforming mixed FEM
multi-term time-fractional mixed diffusion and diffusion-wave equations
L1 time-stepping method
Crank-Nicolson scheme
convergence and superconvergence
Identifying initial value problem for time-fractional diffusion equation with Caputo-like counterpart hyper-Bessel operator: Optimal error bound analysis and regularization method
期刊论文
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 卷号: 44, 期号: 8, 页码: -
作者:
Yang, Fan
;
Sun, Qiao-Xi
;
Li, Xiao-Xiao
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  |  
浏览/下载:11/0
  |  
提交时间:2021/03/12
Errors
Initial value problems
Iterative methods
Numerical methods
Parameterization
Partial differential equations
Bessel operators
Error estimates
Exact solution
Iterative regularization
Optimal error bound
Regularization methods
Regularization parameters
Time fractional diffusion equation
A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations
期刊论文
APPLIED NUMERICAL MATHEMATICS, 2021, 卷号: 159, 页码: 159-173
作者:
Huang, Jianfei
;
Zhang, Jingna
;
Arshad, Sadia
;
Tang, Yifa
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  |  
浏览/下载:13/0
  |  
提交时间:2021/01/14
Multi-term time-space derivatives
Fractional nonlinear diffusion-wave equations
Finite difference schemes
Stability
Convergence
Fast ADI scheme
Investigation on the generalized thermoelastic-diffusive problem with variable properties in three different memory-dependent effect theories
期刊论文
WAVES IN RANDOM AND COMPLEX MEDIA, 2021
作者:
Peng, Wei
;
He, Tianhu
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  |  
浏览/下载:3/0
  |  
提交时间:2022/03/01
Fractional-order derivative
memory-dependent derivative
time-delay factor
kernel function
generalized thermoelastic diffusion theory
variable material properties
The fractional Tikhonov regularization methods for identifying the initial value problem for a time-fractional diffusion equation
期刊论文
Journal of Computational and Applied Mathematics, 2020, 卷号: 380
作者:
Yang, Fan
;
Pu, Qu
;
Li, Xiao-Xiao
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  |  
浏览/下载:9/0
  |  
提交时间:2022/02/17
Initial value problems
Parameterization
Partial differential equations
Columnar axis
Error estimates
Exact solution
Regularization parameters
Symmetric domains
Tikhonov method
Tikhonov regularization method
Time fractional diffusion equation
Error estimate on the tanh meshes for the time fractional diffusion equation
期刊论文
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 页码: 21
作者:
Zhang, Jiali
;
Huang, Jizu
;
Wang, Kun
;
Wang, Xin
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  |  
浏览/下载:9/0
  |  
提交时间:2021/01/14
Caputo fractional derivative
error estimate
the tanh meshes
unconditionally stable
weak singularity
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
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