78 citations · 88 across the 11 of their papers we have counts for
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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation
Anatoly A. Alikhanov, Mohammad Shahbazi Asl, Chengming Huang
This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the deve…
A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation
Guoyu Zhang, Chengming Huang, Anatoly A. Alikhanov +1
The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some esse…
Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion
Min Li, Yaozhong Hu, Chengming Huang +1
In this paper, we study the mean-square stability of the solution and its stochastic theta scheme for the following stochastic differential equations drive by fractional Brownian m…
A second order difference scheme for time fractional diffusion equation with generalized memory kernel
Aslanbek Khibiev, Anatoly Alikhanov, Chengming Huang
In the current work we build a difference analog of the Caputo fractional derivative with generalized memory kernel (L2-1 formula). The fundamental features of this differe…
Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation
Nan Wang, Meng Li, Chengming Huang
In this paper, we consider a second-order scalar auxiliary variable (SAV) Fourier spectral method to solve the nonlinear fractional generalized wave equation. Unconditional energy…
A high-order L2 type difference scheme for the time-fractional diffusion equation
Anatoly A. Alikhanov, Chengming Huang
The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it…
Numerical methods for stochastic Volterra integral equations with weakly singular kernels
Min Li, Chengming Huang, Yaozhong Hu
In this paper, we first establish the existence, uniqueness and Hölder continuity of the solution to stochastic Volterra integral equations with weakly singular kernels. Then, we p…
Compensated projected Euler method for stochastic differential equations with jumps under global monotonicity condition
Min Li, Chengming Huang
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared wi…
Projected Euler method for stochastic delay differential equation under a global monotonicity condition
Min Li, Chengming Huang
This paper investigates projected Euler-Maruyama method for stochastic delay differential equations under a global monotonicity condition. This condition admits some equations with…
A spectral penalty method for two-sided fractional differential equations with general boundary conditions
Nan Wang, Zhiping Mao, Chengming Huang +1
We consider spectral approximations to the conservative form of the two-sided Riemann-Liouville (R-L) and Caputo fractional differential equations (FDEs) with nonhomogeneous Dirich…
An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
Pengde Wang, Chengming Huang
This paper proposes and analyzes an efficient difference scheme for the nonlinear complex Ginzburg-Landau equation involving fractional Laplacian. The scheme is based on the implic…