The article considers symmetric general linear methods, a class of numerical time integration methods which, like symmetric Runge--Kutta methods, are applicable to general time--reversible differential equations, not just those derived from separable second--order problems. A definition of time--reversal symmetry is formulated for general linear methods, and criteria are found for the methods to be free of linear parasitism. It is shown that symmetric parasitism--free methods cannot be explicit, but a method of order $4$ is constructed with only one implicit stage. Several characterizations of symmetry are given, and connections are made with $G$--symplecticity. Symmetric methods are shown to be of even order, a suitable symmetric starting method is constructed and shown to be essentially unique. The underlying one--step method is shown to be time--symmetric. Several symmetric methods of order $4$ are constructed and implemented on test problems. The methods are efficient when compared with Runge--Kutta methods of the same order, and invariants of the motion are well--approximated over long time intervals.
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）
Explicit and Effectively Symmetric Runge-Kutta Methods
Imperial College London（帝国理工学院）；Norwegian University of Science and Technology（挪威科技大学）；Weierstrass Institute for Applied Analysis and Stochastics & Institute for Mathematics, Humboldt University of Berlin（柏林洪堡大学魏尔斯特拉斯应用分析与随机性研究所及数学研究所）
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）
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）
Runge--Kutta convolution coercivity and its use for time-dependent boundary integral equations
The Maxwell Institute for Mathematics in the Sciences（麦克斯韦数理科学研究所）；School of Mathematical & Computer Sciences, Heriot-Watt University（赫瑞-瓦特大学数学与计算机科学学院）；Mathematisches Institut, Universität Tübingen（蒂宾根大学数学研究所）
Numerical Stability of Explicit Runge-Kutta Finite-Difference Schemes for the Nonlinear Schrödinger Equation
Nonlinear Dynamical System Group, Computational Science Research Center（非线性动力系统组，计算科学研究中心）；Department of Mathematics and Statistics, San Diego State University（圣地亚哥州立大学数学与统计系）
Explicit Runge Kutta Methods that Alleviate Order Reduction
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Temple University（天普大学）；New Jersey Institute of Technology（新泽西理工学院）
Local Linearization-Runge Kutta Methods: a class of A-stable explicit integrators for dynamical systems
IMPA（巴西数学研究所）；Universidad de Ciencias Informáticas（古巴信息科学大学）；CIMFAV-DEUV, Facultad de Ciencias, Universidad de Valparaiso（瓦尔帕莱索大学理学院）；Instituto de Cibernética, Matemática y Física（古巴计算机、数学与物理研究所）；Montreal Neurological Institute, McGill University（麦吉尔大学蒙特利尔神经学研究所）
On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems
本文给出了一个系统的理论框架来推导线性半负方程组的一般隐式和显式Runge-Kutta（RK）方法的能量恒等式。推广了[Z. Sun和C.- W. Shu，SIAM J. Numer.肛门，57（2019），pp. 1158-1182]。所建立的能量恒等式提供了关于RK离散化中能量是否以及如何耗散的精确表征，从而导致RK方法的弱稳定性和强稳定性准则。此外，基于一类对称矩阵的解析Cholesky型分解，我们发现了所有对角Pade逼近的统一能量恒等式.矩阵的结构非常复杂，使得发现统一的能量恒等式和证明分解具有很大的挑战性。我们的证明涉及到技术的组合恒等式的建设和新的技术，从理论的超几何级数。我们的框架是由离散模拟的分部积分法技术和连续能量法的一系列扩展。在某些特殊情况下，我们的分析建立了连续和离散能量定律之间的密切联系，增强了我们对其内在机制的理解。给出了几个具体的隐式方法的例子来说明离散能量定律。一些数值例子进一步证实了理论性质。
Positive and elementary stable explicit nonstandard Runge-Kutta methods for a class of autonomous dynamical systems
Center for Informatics and Computing, Vietnam Academy of Science and Technology (VAST)（越南科学技术院信息计算中心）；Institute of Information Technology, Vietnam Academy of Science and Technology (VAST)（越南科学技术院信息技术研究所）
