103 citations · 453 across the 27 of their papers we have counts for
27 papers
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…
A Hessenberg-type Algorithm for Computing PageRank Problems
Xian-Ming Gu, Siu-Long Lei, Ke Zhang +3
PageRank is a widespread model for analysing the relative relevance of nodes within large graphs arising in several applications. In the current paper, we present a cost-effective…
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 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 flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems
Hong-Xiu Zhong, Xian-Ming Gu
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the…
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…
Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously
Xian-Ming Gu, Ting-Zhu Huang, Bruno Carpentieri +3
Multi-shifted linear systems with non-Hermitian coefficient matrices arise in numerical solutions of time-dependent partial/fractional differential equations (PDEs/FDEs), in contro…
Fast iterative method with a second order implicit difference scheme for time-space fractional convection-diffusion equations
Xian-Ming Gu, Ting-Zhu Huang, Cui-Cui Ji +2
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To star…
Block variants of the COCG and COCR methods for solving complex symmetric linear systems with multiple right-hand sides
Xian-Ming Gu, Bruno Carpentieri, Ting-Zhu Huang +1
In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subs…
Restarted Hessenberg method for solving shifted nonsymmetric linear systems
Xian-Ming Gu, Ting-Zhu Huang, Guojian Yin +3
It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual (GMRES) method in several circumstances for solving shifte…
A note on the proofs of generalized radon inequality
Yongtao Li, Xian-Ming Gu, Jianci Xiao
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find math…
The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hölder Inequality
Yongtao Li, Xian-Ming Gu, Jianxing Zhao
In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the Hölder inequality and the weighted power-me…