21 citations · 47 across the 21 of their papers we have counts for
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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…
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 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…
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…
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,…