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• Asymptotic Preserving Spectral Deferred Correction Methods for Hyperbolic Systems with Relaxation

  Chong Sun & Yinhua Xia

  2019-04-04

  46103 3346 Pages:531-557

• On the Spurious Mode Generation Induced by Spectral-Like Optimized Interpolation Schemes Used in Computational Acoustics

  Guilherme Cunha & Stéphane Redonnet

  2018-04-04

  39639 3153 Pages:325-352

• A Class of Second-Order Energy-Stable Schemes for the Cahn-Hilliard Equation and Their Linear Iteration Algorithm

  Xiaohan Zhu, Yuezheng Gong, Yushun Wang

  2025-09-05

  3601 327 Pages:1210-1236

• Conservative and Dissipative Local Discontinuous Galerkin Methods for Korteweg-de Vries Type Equations

  Qian Zhang & Yinhua Xia

  2018-10-11

  45795 3429 Pages:532-563

• Nonstandard Fourier Pseudospectral Time Domain (PSTD) Schemes for Partial Differential Equations

  Bradley E. Treeby, Elliott S. Wise & B. T. Cox

  2018-09-17

  46725 3302 Pages:623-634

• Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems

  Feng Chen & Jie Shen

  2013-05-05

  40934 4750 Pages:1189-1208

• Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations

  Xiaoling Liu & Chuanju Xu

  2018-04-09

  41899 3392 Pages:1408-1428

• Accuracy Enhancement Using Spectral Postprocessing for Differential Equations and Integral Equations

  Tao Tang & Xiang Xu

  2018-04-11

  41737 3634 Pages:779-792

• Benchmark Computation of Morphological Complexity in the Functionalized Cahn-Hilliard Gradient Flow

  Andrew Christlieb, Keith Promislow, Zengqiang Tan, Sulin Wang, Brian Wetton, Steven M. Wise

  2025-04-27

  9308 731 Pages:877-920 Open-access

• On 16th and 32nd Order Multioperators-Based Schemes for Smooth and Discontinuous Fluid Dynamics Solutions

  Andrei I. Tolstykh

  2018-04-09

  41925 3309 Pages:572-598

• An Unconditionally Energy-Stable and Orthonormality-Preserving Scheme for the Kohn-Sham Gradient Flow Based Model Based on a Tetrahedral Spectral Element Method

  Hongfei Zhan, Ting Wang, Guanghui Hu

  2025-04-27

  9276 535 Pages:921-941

• On the Monotonicity of $Q^2$ Spectral Element Method for Laplacian on Quasi-Uniform Rectangular Meshes

  Logan J. Cross, Xiangxiong Zhang

  2024-01-31

  28422 2652 Pages:160-180

• On the Connection Between the Spectral Difference Method and the Discontinuous Galerkin Method

  Georg May

  2011-09-01

  38351 3862 Pages:1071-1080

• On Integral Equation and Least Squares Methods for Scattering by Diffraction Gratings

  T. Arens, S. N. Chandler-Wilde & J. A. DeSanto

  2020-07-31

  38853 3856 Pages:1010-1042

• Fast Kinetic Scheme: Efficient MPI Parallelization Strategy for 3D Boltzmann Equation

  Jacek Narski

  2018-10-11

  44374 3447 Pages:361-389

• A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation

  Ruihan Guo & Yan Xu

  2018-09-17

  67756 5453 Pages:123-151

• Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations

  Haiyang Gao, Z. J. Wang & H. T. Huynh

  2013-08-05

  43683 4128 Pages:1013-1044

• Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems

  Ruihan Guo & Yan Xu

  2019-02-25

  50240 5305 Pages:87-113

• A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations

  Hendrik Ranocha, Dimitrios Mitsotakis, David I. Ketcheson

  2021-02-25

  48435 3403 Pages:979-1029

• Composite Laguerre-Legendre Pseudospectral Method for Exterior Problems

  Tian-Jun Wang & Ben-Yu Guo

  2018-04-11

  42317 3687 Pages:350-375

• High-Order Spectral Simulation of Dispersive Two-Dimensional Materials

  David P. Nicholls, Tianyu Zhu

  2025-09-05

  3651 344 Pages:923-952

• Efficient, Accurate and Energy Stable Discontinuous Galerkin Methods for Phase Field Models of Two-Phase Incompressible Flows

  Ruihan Guo, Yan Xu

  2019-07-02

  49455 3145 Pages:1224-1248

• The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials

  Zhennan Zhou & Giovanni Russo

  2019-04-04

  47389 5448 Pages:469-505 Open-access

• Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations

  Hua Wu, Jiajia Pan & Haichuan Zheng

  2020-07-31

  40974 3300 Pages:1221-1241

• An Efficient Time-Splitting Method to Simulate the Dynamics of Spin-Orbit Coupled Spin-1 Bose-Einstein Condensates

  Xiaolan Chen, Yongjun Yuan, Yong Zhang

  2026-01-15

  2956 188 Pages:119-146

• A Hybrid WENO Scheme for Steady Euler Equations in Curved Geometries on Cartesian Grids

  Yifei Wan, Yinhua Xia

  2023-06-06

  47343 3060 Pages:1270-1331

• On Energy Stable Runge-Kutta Methods for the Water Wave Equation and Its Simplified Non-Local Hyperbolic Model

  Lei Li, Jian-Guo Liu, Zibu Liu, Yi Yang, Zhennan Zhou

  2022-07-06

  42935 3698 Pages:222-258