A Fourier Pseudospectral Method for the "Good" Boussinesq Equation with Second Order Temporal Accuracy
School of Science, Southwest University of Science and Technology（西南科技大学理学院）；Department of Mathematics, University of Tennessee（田纳西大学数学系）；Mathematics Department, University of Massachusetts（马萨诸塞大学数学系）
Kelong Cheng, Wenqiang Feng, Sigal Gottlieb, Cheng Wang
In this paper, we discuss the nonlinear stability and convergence of a fully discrete Fourier pseudospectral method coupled with a specially designed second order time-stepping for the numerical solution of the "good" Boussinesq equation. Our analysis improves the existing results presented in earlier literature in two ways. First, an $l_\infty(0, T^*; H2)$ convergence for the solution and $l_\infty(0, T^*; l_2)$ convergence for the time-derivative of the solution are obtained in this paper, instead of the $l_\infty(0, T^*; l_2)$ convergence for the solution and the $l_\infty(0, T^*; H^{-2})$ convergence for the time-derivative, given in [17]. In addition, the stability and convergence of this method is shown to be unconditional for the time step in terms of the spatial grid size, compared with a severe restriction time step restriction $Δt \leq Ch^2$ reported in [17].
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
National University of Singapore（新加坡国立大学）；NUS Graduate School for Integrative Sciences and Engineering (NGS), National University of Singapore（新加坡国立大学整合科学与工程研究生学院）
Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime
Beijing Computational Science Research Center（北京计算科学研究中心）；IRMAR, Université de Rennes 1（雷恩第一大学 IRMAR）
Pseudospectral method for solving PDEs using Matrix Product States
Institute of Fundamental Physics IFF-CSIC（基础物理研究所）；Millennium Institute for Research in Optics（光学研究千年研究所）；Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción（康塞普西翁大学物理与数学科学学院）
Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
National University of Singapore（新加坡国立大学）；New Jersey Institute of Technology（新泽理工学院）；Université de Lorraine（洛林大学）；Inria Nancy Grand-Est（法国国家信息与自动化研究院南斯特大东部中心）；University Wien（维也纳大学）
A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime
National University of Singapore（新加坡国立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Purdue University（普渡大学）；Université de Lorraine（洛林大学）；Inria Nancy-Grand Est（南锡大东部国家研究学院）
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
VU University Amsterdam（阿姆斯特丹自由大学）；Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo（圣保罗大学数学与计算科学学院）；Université Laval, Département de Mathématiques et de Statistique（拉瓦尔大学数学与统计系）
A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime
A potential projection method for the nonlinear Schrödinger equation with low regularity potential
National University of Singapore（新加坡国立大学）；Zhiyuan College and School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学致远学院数学系）；Department of Statistics and CCAM, University of Chicago（芝加哥大学统计与计算连续物质应用中心）
A Uniformly Accurate Multiscale Time Integrator for the Klein-Gordon-Schrödinger Equations in the Nonrelativistic Regime via Simplified Transmission Conditions
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Mathematics, National University of Singapore（新加坡国立大学数学系）
Numerical approximation to Benjamin type equations. Generation and stability of solitary waves
University of Athens（雅典大学）；Institute of Applied & Computational Mathematics, FO.R.T.H.（应用与计算数学研究所，FO.R.T.H.）；University of Valladolid（巴利亚多利德大学）；Victoria University of Wellington（惠灵顿维多利亚大学）
A uniformly accurate multiscale time integrator for the nonlinear Klein-Gordon equation in the nonrelativistic regime via simplified transmission conditions
High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime
Xi’an Jiaotong University（西安交通大学）；Hebei Normal University（河北师范大学）
