19 citations · 80 across the 17 of their papers we have counts for
17 papers
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…
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…
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…
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…
Finite difference method for inhomogeneous fractional Dirichlet problem
Jing Sun, Weihua Deng, Daxin Nie
We make the split of the integral fractional Laplacian as , where . Based on this splitting, we respectively discr…
Strong convergence order for the scheme of fractional diffusion equation driven by fractional Gaussion noise
Daxin Nie, Jing Sun, Weihua Deng
Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index , it has positive correlation reflecting a persistent autocorrelation struc…
High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth data
Jing Sun, Daxin Nie, Weihua Deng
The Feynman-Kac equation governs the distribution of the statistical observable -- functional, having wide applications in almost all disciplines. After overcoming challenges from…
Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data
Jing Sun, Daxin Nie, Weihua Deng
In this paper, we are concerned with the numerical solution for the backward fractional Feynman-Kac equation with non-smooth initial data. Here we first provide the regularity esti…
Numerical algorithm for the model describing anomalous diffusion in expanding media
Daxin Nie, Jing Sun, Weihua Deng
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96}…
Numerical algorithm for the space-time fractional Fokker-Planck system with two internal states
Daxin Nie, Jing Sun, Weihua Deng
The fractional Fokker-Planck system with multiple internal states is derived in [Xu and Deng, Math. Model. Nat. Phenom., , 10 (2018)], where the space derivative is La…
Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative
Jing Sun, Daxin Nie, Weihua Deng
Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723],…
Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal states
Daxin Nie, Jing Sun, Weihua Deng
Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distri…
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…
Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes
Daxin Nie, Jing Sun, Weihua Deng
This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both r…
A reduced finite element formulation for space fractional partial differential equation
Jing Sun, Daxin Nie, Weihua Deng
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly red…
Algorithm implementation and numerical analysis for the two-dimensional tempered fractional Laplacian
Jing Sun, Daxin Nie, Weihua Deng
Tempered fractional Laplacian is the generator of the tempered isotropic Lévy process [W.H. Deng, B.Y. Li, W.Y. Tian, and P.W. Zhang, Multiscale Model. Simul., 16(1), 125-149, 2018…