School of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；School of Mathematics and Information Science, Henan Polytechnic University（河南理工大学数学与信息科学学院）
We develop continuous-stage Runge-Kutta-Nyström (csRKN) methods for solving second order ordinary differential equations (ODEs) in this paper. The second order ODEs are commonly encountered in various fields and some of them can be reduced to the first order ODEs with the form of separable Hamiltonian systems. The symplecticity-preserving numerical algorithm is of interest for solving such special systems. We present a sufficient condition for a csRKN method to be symplecticity-preserving, and by using Legendre polynomial expansion we show a simple way to construct such symplectic RKN type method.
College of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering（湖南省工程数学建模与分析重点实验室）
Efficient Order-Optimal Preconditioners for Implicit Runge-Kutta and Runge-Kutta-Nyström Methods Applicable to a Large Class of Parabolic and Hyperbolic PDEs
我们概括了Mardal，Nilssen和Staff（2007，SIAM J. Sci.第29页。361-375）和Rana，Howle，Long，Meek，and Milestone（2021，SIAM J. Sci. Comp. v. 43，p. 475-495）关于抛物型偏微分方程的阶最优预条件子到更大类的微分方程和方法。所考虑的问题是那些形式$u_{t}=-\mathcal{K}u+g$和$u_{tt}=-\mathcal{K}u+g$，其中运营商$\mathcal{K}$是由$\mathcal{K}u:=-\nabla\cdot\left(α\nabla u\right)+βu$和功能$α$和$β$定义的限制，使$α>0$，和$β\ge0$。所考虑的方法是抛物型方程的A-稳定隐式龙格-库塔法和双曲型方程的隐式Runge-Kutta-Nyström法。我们证明了由这些问题产生的阶段方程组的一类块预条件子的阶最优性，并进一步证明了Rana等人的LD和DU预条件子也属于这类预条件子.我们进行了几个测试问题的数值实验在这个类-二维扩散方程，Pennes生物热方程，波动方程，和Klein-Gordon方程，常系数和变系数。我们的实验表明，这些预条件，特别是LD预条件，是成功的减少系统的条件数，以及提高GMRES应用于阶段方程的收敛速度和求解时间。
High order symplectic integrators based on continuous-stage Runge-Kutta Nystrom methods
College of Mathematics and Statistics, Changsha University of Science and Technology（长沙理工大学数学与统计学院）；LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）；School of Science, East China Jiaotong University（华东交通大学理学院）
Runge-Kutta semidiscretizations for stochastic Maxwell equations with additive noise
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算力学研究所）
Conjugate-symplecticity properties of Euler--Maclaurin methods and their implementation on the Infinity Computer
Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；Università della Calabria（卡拉布里亚大学）；Lobachevsky State University of Nizhni Novgorod（下诺夫哥罗德洛巴切夫斯基州立大学）
Symplectic Runge-Kutta Semi-discretization for Stochastic Schrödinger Equation
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学/工程计算国家重点实验室）
High-Order Nyström/Convolution-Quadrature Solution of Time-Domain Scattering from Closed and Open Lipschitz Boundaries with Dirichlet and Neumann Boundary Conditions
Symmetric-adjoint and symplectic-adjoint methods and their applications
Institute of Mathematics, Chinese Academy of Sciences（中国科学院数学研究所）；School of Mathematics and Statistics, Central South University（中南大学数学与统计学院）；Department of Mathematics, Hong Kong Baptist University（香港浸会大学数学系）
A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian systems
Qufu Normal University（曲阜师范大学）；University of Tübingen（蒂宾根大学）；Nanjing University（南京大学）
