376 citations · 1.1k across the 23 of their papers we have counts for
6 papers · 1 filter
Sharp -norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
Jincheng Ren, Hong-lin Liao, Jiwei Zhang +1
Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional -norm analysis (corresponding to th…
A Unified Gas-kinetic Particle Method for Multiscale Photon Transport
Weiming Li, Chang Liu, Yajun Zhu +2
In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes f…
Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations
Hong-lin Liao, Yonggui Yan, Jiwei Zhang
A fast two-level linearized scheme with unequal time-steps is constructed and analyzed for an initial-boundary-value problem of semilinear subdiffusion equations. The two-level fas…
Superconvergence Points of Integer and Fractional Derivatives of Special Hermite Interpolations and Its Applications in Solving FDEs
Beichuan Deng, Jiwei Zhang, Zhimin Zhang
In this paper, we study convergence and superconvergence theory of integer and fractional derivatives of the one-point and the two-point Hermite interpolations. When considering th…
A discrete Grönwall inequality with application to numerical schemes for subdiffusion problems
Hong-lin Liao, William McLean, Jiwei Zhang
We consider a class of numerical approximations to the Caputo fractional derivative. Our assumptions permit the use of nonuniform time steps, such as is appropriate for accurately…
A second-order scheme with nonuniform time steps for a linear reaction-sudiffusion problem
Hong-lin Liao, William McLean, Jiwei Zhang
Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approxi…