61 citations · 285 across the 19 of their papers we have counts for
19 papers
Splitting-based randomized dynamical low-rank approximations for stiff matrix differential equations
Zi Wu, Yong-Liang Zhao, Xian-Ming Gu
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semili…
A Generalized Block Circulant Preconditioner for Crank-Nicolson All-at-Once Systems with Applications to Option Pricing PDEs
Yong-Liang Zhao, Yao Li, Xian-Ming Gu +1
The Crank--Nicolson (CN) method is a widely used time integration scheme for evolutionary partial differential equations (PDEs) arising in various scientific and engineering discip…
A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms
Yong-Liang Zhao, Xian-Ming Gu
Damped wave equations have been used in many real-world fields. In this paper, we study a low-rank solution of the strongly damped wave equation with the damping term, visco-elasti…
A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model
Jinfeng Zhou, Xian-Ming Gu, Yong-Liang Zhao +1
The Black-Scholes (B-S) equation has been recently extended as a kind of tempered time-fractional B-S equations, which becomes an interesting mathematical model in option pricing.…
An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation
Yong-Liang Zhao, Xian-Ming Gu
The extended Fisher--Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biology systems. In this paper, we propose a full-rank splitting s…
On the bilateral preconditioning for an L2-type all-at-once system arising from time-space fractional Bloch-Torrey equations
Yong-Liang Zhao, Xian-Ming Gu, Hu Li
Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this pa…
An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation
Yong-Liang Zhao, Meng Li, Alexander Ostermann +1
The space fractional Cahn-Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn-Hilliard m…
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
Yong-Liang Zhao, Alexander Ostermann, Xian-Ming Gu
Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integra…
A preconditioning technique for an all-at-once system from Volterra subdiffusion equations with graded time steps
Yong-Liang Zhao, Xian-Ming Gu, Alexander Ostermann
Volterra subdiffusion problems with weakly singular kernel describe the dynamics of subdiffusion processes well.The graded scheme is often chosen to discretize such problems s…
Fast second-order implicit difference schemes for time distributed-order and Riesz space fractional diffusion-wave equations
Huan-Yan Jian, Ting-Zhu Huang, Xian-Ming Gu +2
In this paper, fast numerical methods are established for solving a class of time distributed-order and Riesz space fractional diffusion-wave equations. We derive new difference sc…
A note on parallel preconditioning for the all-at-once solution of Riesz fractional diffusion equations
Xian-Ming Gu, Yong-Liang Zhao, Xi-Le Zhao +2
The -step backwards difference formula (BDF) for solving the system of ODEs can result in a kind of all-at-once linear systems, which are solved via the parallel-in-time precond…
Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
Xian-Ming Gu, Hai-Wei Sun, Yanzhi Zhang +1
In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplac…
A fast implicit difference scheme for solving the generalized time-space fractional diffusion equations with variable coefficients
Xian-Ming Gu, Ting-Zhu Huang, Yong-Liang Zhao +2
In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coeff…
An implicit integration factor method for a kind of spatial fractional diffusion equations
Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu +2
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order…
A preconditioning technique for all-at-once system from the nonlinear tempered fractional diffusion equation
Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu +2
An all-at-once linear system arising from the nonlinear tempered fractional diffusion equation with variable coefficients is studied. Firstly, the nonlinear and linearized implicit…
A fast second-order accurate difference schemes for time distributed-order and Riesz space fractional diffusion equations
Huan-Yan Jian, Ting-Zhu Huang, Xi-Le Zhao +1
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion e…
A limited-memory block bi-diagonal Toeplitz preconditioner for block lower triangular Toeplitz system from time-space fractional diffusion equation
Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu +2
A block lower triangular Toeplitz system arising from time-space fractional diffusion equation is discussed. For efficient solutions of such the linear system, the preconditioned b…
A second-order accurate implicit difference scheme for time fractional reaction-diffusion equation with variable coefficients and time drift term
Yong-Liang Zhao, Pei-Yong Zhu, Xian-Ming Gu +1
An implicit finite difference scheme based on the - formula is presented for a class of one-dimensional time fractional reaction-diffusion equations with variable coeffici…
A fast second-order implicit difference method for time-space fractional advection-diffusion equation
Yong-Liang Zhao, Ting-Zhu Huang, Xian-Ming Gu +1
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equati…