Zobrazeno 1 - 10
of 526
pro vyhledávání: '"Zhao, Yong‐Liang"'
The Crank-Nicolson (CN) method is a well-known time integrator for evolutionary partial differential equations (PDEs) arising in many real-world applications. Since the solution at any time depends on the solution at previous time steps, the CN metho
Externí odkaz:
http://arxiv.org/abs/2401.16113
Autor:
Zhao, Yong-Liang, Gu, Xian-Ming
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-elastic damping term and mass term. Firstly, a second-order finite differenc
Externí odkaz:
http://arxiv.org/abs/2308.08888
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. In this study, we provide a fast numerical method to approximate the s
Externí odkaz:
http://arxiv.org/abs/2303.10592
Autor:
Zhao, Yong-Liang, Gu, Xian-Ming
Publikováno v:
Journal of Computational Physics, 2024
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 scheme and a rank-adaptive splitting approach for this equation. We fir
Externí odkaz:
http://arxiv.org/abs/2210.15900
Publikováno v:
Computers and Mathematics with Applications, 2023
Time-space fractional Bloch-Torrey equations (TSFBTEs) are developed by some researchers to investigate the relationship between diffusion and fractional-order dynamics. In this paper, we first propose a second-order implicit difference scheme for TS
Externí odkaz:
http://arxiv.org/abs/2109.06510
Autor:
Zhao, Yong-Liang, Gu, Xian-Ming
Publikováno v:
In Journal of Computational Physics 1 June 2024 506
Publikováno v:
In Applied Mathematics and Computation 1 February 2024 462
Publikováno v:
BIT Numerical Mathematics, 2021
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 model. In this article, we propose a temporal second-order energy stabl
Externí odkaz:
http://arxiv.org/abs/2011.02106
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
Publikováno v:
Journal of Computational Physics, 2021
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 integration method for solving space fractional Ginzburg-Landau equations bas
Externí odkaz:
http://arxiv.org/abs/2010.05249
Publikováno v:
Journal of Scientific Computing, 2021
Volterra subdiffusion problems with weakly singular kernel describe the dynamics of subdiffusion processes well.The graded $L1$ scheme is often chosen to discretize such problems since it can handle the singularity of the solution near $t = 0$. In th
Externí odkaz:
http://arxiv.org/abs/2007.14636