58 citations · 143 across the 19 of their papers we have counts for
13 papers · 1 filter
High-order nonuniform time-stepping and MBP-preserving linear schemes for the time-fractional Allen-Cahn equation
Bingyin Zhang, Hongfei Fu
In this paper, we present a class of nonuniform time-stepping, high-order linear stabilized schemes that can preserve both the discrete energy stability and maximum-bound principle…
Analysis and Petrov-Galerkin numerical approximation for variable coefficient two-sided fractional diffusion, advection, reaction equations
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion…
Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution…
A fast method for variable-order space-fractional diffusion equations
Jinhong Jia, Xiangcheng Zheng, Hong Wang
We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due t…
Optimal order finite element approximations for variable-order time-fractional diffusion equations
Xiangcheng Zheng, Fanhai Zeng, Hong Wang
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are prove…
Numerical approximations for the variable coefficient fractional diffusion equations with non-smooth data
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffus…
Data-driven physics informed deep learning of solute transport with anomalous diffusion
Huan Liu, Hong Wang, Xiangcheng Zheng
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-r…
Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral opera…
Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown . By introducing an intermediate unknown,…
A fast solver for spectral element approximation applied to fractional differential equations using hierarchical matrix approximation
Xianjuan Li, Zhiping Mao, Fangying Song +2
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the…
Fractional Gray-Scott Model: Well-posedness, Discretization, and Simulations
Tingting Wang, Fangying Song, Hong Wang +1
The Gray-Scott (GS) model represents the dynamics and steady state pattern formation in reaction-diffusion systems and has been extensively studied in the past. In this paper, we c…
A comparative study on nonlocal diffusion operators related to the fractional Laplacian
Siwei Duo, Hong Wang, Yanzhi Zhang
In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operato…
Wellposedness and regularity of steady-state two-sided variable-coefficient conservative space-fractional diffusion equations
Danping Yang, Hong Wang
We study the Dirichlet boundary-value problem of steady-state two-sided variable-coefficient conservative space-fractional diffusion equations. We show that the Galerkin weak formu…