In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian PDEs. This approach is based on the temporal discretization using continuous Runge-Kutta-type methods, and the spatial discretization using pseudospectral methods or Gauss--Legendre collocation methods. The local energy conservation law of our new schemes is analyzed in detail. The effectiveness of the novel local energy-preserving integrators is demonstrated by coupled nonlinear Schrödinger equations and 2D nonlinear Schrödinger equations with external fields. Our new schemes are compared with some classical multi-symplectic and symplectic schemes in numerical experiments. The numerical results show the remarkable \emph{long-term} behaviour of our new schemes.
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）
Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs
Institute of Mathematics, Czech Academy of Sciences（捷克科学院数学研究所）；School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究学院特里凡得琅数学学院）
Preservation of stability properties near fixed points of linear hamiltonian systems by symplectic integrators
Harbin Institute of Technology（哈尔滨工业大学）；University of Washington（华盛顿大学）；Academy of Mathematics and System Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
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）
Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise
Universite de Pau et des Pays de l’Adour, E2S UPPA（波城大学）；Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学）；Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Swedish Defence Research Agency (FOI)（瑞典国防研究局）
Fast symplectic integrator for Nesterov-type acceleration method
Center of Mathematics for Artificial Intelligence and Data Science（人工智能与数据科学数学中心）；Chubu University（中部大学）；The Institute of Statistical Mathematics（统计数学研究所）；RIKEN AIP（理化学研究所先进智能项目中心）
Stochastic K-symplectic integrators for stochastic non-canonical Hamiltonian systems and applications to the Lotka--Volterra model
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）；School of Science, East China Jiaotong University（华东交通大学理学院）
Multi-symplectic Preserving Integrator for the Schrödinger Equation with Wave Operator
Jiangxi Normal University（江西师范大学）；Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS（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）
Exponential Stability Estimate of Symplectic Integrators for Integrable Hamiltonian Systems
Inner Mongolia University（内蒙古大学）；Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学研究所）；South China University of Technology（华南理工大学）
High precision Symplectic Integrators for the Solar System
Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR8028, Observatoire de Paris, UPMC（巴黎天文动力学与系统研究所）；Instituto de Matemática Multidisciplinar, Universitat Politécnica de València（瓦伦西亚理工大学多学科数学研究所）；Institut de Matemàtiques i Aplicacions de Castelló and Departament de Matemàtiques, Universitat Jaume I（卡斯特利翁数学与应用研究所及马德里卡洛斯三世大学数学系）；Konputazio Zientziak eta A.A. saila, Informatika Fakultatea, EHU/UPV（巴斯克大学计算机学院）
Numerical Construction of Quasi-Periodic Solutions Beyond Symplectic Integrators
University of Chinese Academy of Sciences（中国科学院大学）；Fudan University（复旦大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences（上海数学与交叉学科研究院）
