Energy estimates for two-dimensional space-Riesz fractional wave equation
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University（兰州大学数学与统计学院、甘肃省应用数学与复杂系统重点实验室）
分数波方程 governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic viscoelasticity. In this paper, we first develop the energy method to estimate the one-dimensional space-Riesz fractional wave equation. For two-dimensional cases with the variable coefficients, the discretized matrices are proved to be commutative, which ensures to carry out of the priori error estimates. The unconditional stability and convergence with the global truncation error $\mathcal{O}(τ^2+h^2)$ are theoretically proved and numerically verified. In particulary, the framework of the priori error estimates and convergence analysis are still valid for the compact finite difference scheme and the nonlocal wave equation.
英文摘要：
The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic viscoelasticity. In this paper, we first develop the energy method to estimate the one-dimensional space-Riesz fractional wave equation. For two-dimensional cases with the variable coefficients, the discretized matrices are proved to be commutative, which ensures to carry out of the priori error estimates. The unconditional stability and convergence with the global truncation error $\mathcal{O}(τ^2+h^2)$ are theoretically proved and numerically verified. In particulary, the framework of the priori error estimates and convergence analysis are still valid for the compact finite difference scheme and the nonlocal wave equation.
On $τ$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients
Hanshan Normal University（韩山师范学院）；Southwestern University of Finance and Economics（西南财经大学）；University of Insubria（因苏布里亚大学）；University of Uppsala（乌普萨拉大学）
Superconvergence Points For The Spectral Interpolation Of Riesz Fractional Derivatives
Wayne State University（韦恩州立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Department of Mathematics, Wayne State University（韦恩州立大学数学系）；School of Mathematics, Southeast University（东南大学数学学院）
Jacobi-Galerkin spectral method for eigenvalue problems of Riesz fractional differential equations
Beijing Computational Sciences and Research Center（北京计算科学研究中心）；Division of Applied Mathematics, Brown University（布朗大学应用数学系）；State Key Laboratory of Computer Science/Laboratory of Parallel Computing, Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）
Fully Finite Element Adaptive Algebraic Multigrid Method for Time-Space Caputo-Riesz Fractional Diffusion Equations
School of Mathematics and Computational Science, Xiangtan University（湘潭大学数学与计算科学学院）；Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University（湘潭大学湖南省科学与工程计算重点实验室）
