381 citations · 1k across the 39 of their papers we have counts for
40 papers
The Contour integral method for Feynman-Kac equation with two internal states
Fugui Ma, Lijing Zhao, Yejuan Wang +1
We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states [P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10]…
Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution
Daxin Nie, Jing Sun, Weihua Deng
Finite difference method as a popular numerical method has been widely used to solve fractional diffusion equations. In the general spatial error analyses, an assumption $u\in C^{4…
Analyses of the contour integral method for time fractional subdiffusion-normal transport equation
Fugui Ma, Lijing Zhao, Weihua Deng +1
In this work, we theoretically and numerically discuss the time fractional subdiffusion-normal transport equation, which depicts a crossover from sub-diffusion (as …
Optimal convergence for the regularized solution of the model describing the competition between super- and sub- diffusions driven by fractional Brownian sheet noise
Jing Sun, Daxin Nie, Weihua Deng
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competitio…
A sharp -robust scheme on graded meshes for two-dimensional time tempered fractional Fokker-Planck equation
Can Wang, Weihua Deng, Xiangong Tang
In this paper, we are concerned with the numerical solution for the two-dimensional time fractional Fokker-Planck equation with tempered fractional derivative of order . Althoug…
Numerical method for the Fokker-Planck equation of Brownian motion subordinated by inverse tempered stable subordinator with drift
Xiangong Tang, Can Wang, Weihua Deng
In this work, based on the complete Bernstein function, we propose a generalized regularity analysis including maximal regularity for the Fokker--Planck equation, wh…
Local discontinuous Galerkin method for the Backward Feynman-Kac Equation
Dong Liu, Weihua Deng
Anomalous diffusions are ubiquitous in nature, whose functional distributions are governed by the backward Feynman-Kac equation. In this paper, the local discontinuous Galerkin (LD…
Numerical Approximation for Stochastic Nonlinear Fractional Diffusion Equation Driven by Rough Noise
Daxin Nie, Jing Sun, Weihua Deng
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spati…
Regularity theory and numerical algorithm for the fractional Klein-Kramers equation
Jing Sun, Daxin Nie, Weihua Deng
Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for fractional Klein-Kramers equation based on…
Lévy walk dynamics in non-static media
Tian Zhou, Pengbo Xu, Weihua Deng
Almost all the media the particles move in are non-static. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement of the media, sometime…
Numerical approximations for the fractional Fokker-Planck equation with two-scale diffusion
Jing Sun, Weihua Deng, Daxin Nie
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equa…
Gaussian Process and Levy Walk under Stochastic Non-instantaneous Resetting and Stochastic Rest
Tian Zhou, Pengbo Xu, Weihua Deng
A stochastic process with movement, return, and rest phases is considered in this paper. For the movement phase, the particles move following the dynamics of Gaussian process or ba…
Lévy-walk-like Langevin dynamics affected by a time-dependent force
Yao Chen, Weihua Deng
Lévy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of…
Higher order approximation for stochastic wave equation
Xing Liu, Weihua Deng
The infinitesimal generator (fractional Laplacian) of a process obtained by subordinating a killed Brownian motion catches the power-law attenuation of wave propagation. This paper…
Numerical approximation for fractional diffusion equation forced by a tempered fractional Gaussian noise
Xing Liu, Weihua Deng
This paper discusses the fractional diffusion equation forced by a tempered fractional Gaussian noise. The fractional diffusion equation governs the probability density function of…
Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
Xudong Wang, Yao Chen, Weihua Deng
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents by measur…
Langevin picture of Lévy walk in a constant force field
Yao Chen, Xudong Wang, Weihua Deng
Lévy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the Lévy walk with the exponent of the powe…
Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential
Xudong Wang, Yao Chen, Weihua Deng
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic…
Aging two-state process with Lévy walk and Brownian motion
Xudong Wang, Yao Chen, Weihua Deng
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and ha…
Subdiffusion in an external force field
Yao Chen, Xudong Wang, Weihua Deng
The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential,…
Ergodic properties of heterogeneous diffusion processes in a potential well
Xudong Wang, Weihua Deng, Yao Chen
Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity . We investigate the ergodic and non-ergodic behav…
First exit and Dirichlet problem for the nonisotropic tempered -stable processes
Xing Liu, Weihua Deng
This paper discusses the first exit and Dirichlet problems of the nonisotropic tempered -stable process . The upper bounds of all moments of the first exit position $\left|…
Langevin dynamics for Lévy walk with memory
Yao Chen, Xudong Wang, Weihua Deng
Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive…
Central local discontinuous Galerkin method for the space fractional diffusion equation
Jing Sun, Daxin Nie, Weihua Deng
This paper provides the semi-discrete scheme by the central local discontinuous Galerkin method for space fractional diffusion equation on two sets of overlapping cells, and then w…