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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：53/0  |  提交时间：2023/02/07
Physics -informed neural networks  Fractional Laplacian  Nonlocal operators  Uncertainty quantification  
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
收藏  |  浏览/下载：61/0  |  提交时间：2023/02/07
Uncertainty quantification  Anomalous transport  Quasi Monte Carlo simulation  Generalized polynomial chaos  Long-time integration  Poly-fractonomials  
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
收藏  |  浏览/下载：162/0  |  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
收藏  |  浏览/下载：137/0  |  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  
Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion 期刊论文
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 卷号: 130, 期号: 5, 页码: 2675-2692
作者:  Hong, Jialin;  Huang, Chuying;  Kamrani, Minoo;  Wang, Xu
收藏  |  浏览/下载：155/0  |  提交时间：2020/06/30
Cox-Ingersoll-Ross model  Fractional Brownian motion  Backward Euler scheme  Optimal strong convergence rate  Malliavin calculus  
On regularized Hermitian splitting iteration methods for solving discretized almost-isotropic spatial fractional diffusion equations 期刊论文
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2020, 卷号: 27, 期号: 1, 页码: 21
作者:  Bai, Zhong-Zhi;  Lu, Kang-Ya
收藏  |  浏览/下载：160/0  |  提交时间：2020/06/30
convergence property  matrix splitting iteration  preconditioning  spatial fractional diffusion equation  
Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance 期刊论文
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2019, 卷号: 29, 期号: 13, 页码: 4384-4401
作者:  Zhou, Hua-Cheng;  Lv, Chunwan;  Guo, Bao-Zhu;  Chen, YangQuan
收藏  |  浏览/下载：167/0  |  提交时间：2020/01/10
active disturbance rejection control (ADRC)  Mittag-Leffler stabilization  time-fractional anomalous diffusion equation  
Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations 期刊论文
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2019, 卷号: 9, 期号: 3, 页码: 538-557
作者:  Huang, Jianfei;  Arshad, Sadia;  Jiao, Yandong;  Tang, Yifa
收藏  |  浏览/下载：167/0  |  提交时间：2020/01/10
Fractional diffusion-wave equation  nonlinear source  convolution quadrature  generating function  stability and convergence  
On banded M-splitting iteration methods for solving discretized spatial fractional diffusion equations 期刊论文
BIT NUMERICAL MATHEMATICS, 2019, 卷号: 59, 期号: 1, 页码: 1-33
作者:  Bai, Zhong-Zhi;  Lu, Kang-Ya
收藏  |  浏览/下载：109/0  |  提交时间：2019/12/13
Matrix splitting  Iteration method  Convergence property  Spatial fractional diffusion equation  
ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS 期刊论文
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2019, 卷号: 37, 期号: 3, 页码: 297-315
作者:  Huang, Jianfei;  Zhao, Yue;  Arshad, Sadia;  Li, Kuangying;  Tang, Yifa
收藏  |  浏览/下载：180/0  |  提交时间：2019/03/05
Time fractional super-diffusion equation  Nonlinear system  ADI schemes  Stability  Convergence