376 citations · 1.1k across the 23 of their papers we have counts for
23 papers
-robust error estimates of general non-uniform time-step numerical schemes for reaction-subdiffusion problems
Jiwei Zhang, Zhimin Zhang, Chengchao Zhao
Numerous error estimates have been carried out on various numerical schemes for subdiffusion equations. Unfortunately most error bounds suffer from a factor or ,…
Fully Conservative Difference Schemes for the Rotation-Two-Component Camassa-Holm System with Smooth/Nonsmooth Initial Data
Tong Yan, Jiwei Zhang, Qifeng Zhang
The rotation-two-component Camassa--Holm system, which possesses strongly nonlinear coupled terms and high-order differential terms, tends to have continuous nonsmooth solitary wav…
Second order convergence of a modified MAC scheme for Stokes interface problems
Haixia Dong, Zhongshu Zhao, Shuwang Li +2
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and num…
High performance implementation of 3D FEM for nonlocal Poisson problem with different ball approximation strategies
Gengjian Chen, Yuheng Ma, Jiwei Zhang
Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of queries and invoke operations on the meshes.…
Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations
Jihong Wang, Jerry Zhijian Yang, Jiwei Zhang
The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered.…
A unconditionally energy dissipative, adaptive IMEX BDF2 scheme and its error estimates for Cahn-Hilliard equation on generalized SAV approach
Yifan Wei, Jiwei Zhang, Chengchao Zhao +1
An adaptive implicit-explicit (IMEX) BDF2 scheme is investigated on generalized SAV approach for the Cahn-Hilliard equation by combining with Fourier spectral method in space. It i…
On perfectly matched layers of nonlocal wave equations in unbounded multi-scale media
Yu Du, Jiwei Zhang
A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML pr…
Sharp error estimate of variable time-step IMEX BDF2 scheme for parabolic integro-differential equations with initial singularity arising in finance
Chengchao Zhao, Ruoyu Yang, Yana Di +1
The recently developed technique of DOC kernels has been a great success in the stability and convergence analysis for BDF2 scheme with variable time steps. However, such an analys…
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations
Chengchao Zhao, Nan Liu, Yuheng Ma +1
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is construct…
Perfectly Matched Layers for nonlocal Helmholtz equations II: multi-dimensional cases
Yu Du, Jiwei Zhang
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modific…
Sharp pointwise-in-time error estimate of L1 scheme for nonlinear subdiffusion equations
Dongfang Li, Hongyu Qin, Jiwei Zhang
An essential feature of the subdiffusion equations with the -order time fractional derivative is the weak singularity at the initial time. The weak regularity of the solution is…
Numerical solution of a one-dimensional nonlocal Helmholtz equation by Perfectly Matched Layers
Yu Du, Jiwei Zhang
We consider the computation of a nonlocal Helmholtz equation by using Perfectly Matched Layer (PML). We first derive the nonlocal PML equation by extending PML modifications from t…
Exact artificial boundary conditions of 1D semi-discretized peridynamics
Songsong Ji, Gang Pang, Jiwei Zhang +2
The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. It is not trivial to…
Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport
Weiming Li, Chang Liu, Yajun Zhu +2
In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multiscale photon transport. In this method, the photon free streaming and scattering processes…
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…
Analysis of -Galerkin FEMs for time-fractional nonlinear parabolic problems
Dongfang Li, Hong-lin Liao, Weiwei Sun +2
This paper is concerned with numerical solutions of time-fractional nonlinear parabolic problems by a class of -Galerkin finite element methods. The analysis of methods fo…
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations
Shidong Jiang, Jiwei Zhang, Qian Zhang +1
We present an efficient algorithm for the evaluation of the Caputo fractional derivative of order , which can be expressed as a convolution of …
A unified approach to split absorbing boundary conditions for nonlinear Schrödinger equations
Jiwei Zhang, Zhenli Xu, Xiaonan Wu
An efficient method is proposed for numerical solutions of nonlinear Schrödinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equati…