21 citations · 47 across the 21 of their papers we have counts for
22 papers
Numerical analysis of high-order methods for variable-exponent fractional diffusion-wave equation
Wenlin Qiu, Xiangcheng Zheng
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying…
Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control
Yiqun Li, Hong Wang, Xiangcheng Zheng
We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor…
Error estimate for semi-implicit method of sphere-constrained high-index saddle dynamics
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We prove error estimates for the semi-implicit numerical scheme of sphere-constrained high-index saddle dynamics, which serves as a powerful instrument in finding saddle points and…
A generalized fractional Laplacian
Xiangcheng Zheng, V. J. Ervin, Hong Wang
In this article we show that the fractional Laplacian in can be factored into a product of the divergence operator, a Riesz potential operator, and the gradient operator. U…
A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We propose a model-free shrinking-dimer saddle dynamics for finding any-index saddle points and constructing the solution landscapes, in which the force in the standard saddle dyna…
Mathematical and numerical analysis to shrinking-dimer saddle dynamics with local Lipschitz conditions
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We present a mathematical and numerical investigation to the shrinkingdimer saddle dynamics for finding any-index saddle points in the solution landscape. Due to the dimer approxim…
Discretization and index-robust error analysis for constrained high-index saddle dynamics on high-dimensional sphere
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle points confined on the high-dimensio…
Convergence analysis of discrete high-index saddle dynamics
Yue Luo, Xiangcheng Zheng, Xiangle Cheng +1
Saddle dynamics is a time continuous dynamics to efficiently compute the any-index saddle points and construct the solution landscape. In practice, the saddle dynamics needs to be…
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…
Error estimates for Euler discretization of high-index saddle dynamics
Lei Zhang, Pingwen Zhang, Xiangcheng Zheng
High-index saddle dynamics provides an effective means to compute the any-index saddle points and construct the solution landscape. In this paper we prove error estimates for Euler…
Numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method
Xiangcheng Zheng
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discr…
Approximate inversion for Abel integral operators of variable exponent and applications to fractional Cauchy problems
Xiangcheng Zheng
We investigate the variable-exponent Abel integral equations and corresponding fractional Cauchy problems. The main contributions of the work are enumerated as follows: (i) We deve…
Analysis of viscoelastic flow with a generalized memory and its exponential convergence to steady state
Yingwen Guo, Xiangcheng Zheng
We investigate a viscoelastic flow model with a generalized memory, in which a weak-singular component is introduced in the exponential convolution kernel of classical viscoelastic…
Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm
Bing Yu, Lei Zhang, Pingwen Zhang +1
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper,…
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…
Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
Xiangcheng Zheng, Jin Cheng, Hong Wang
We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the sm…
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,…