Search Results

• Numerical Methods for Solving the Hartree-Fock Equations of Diatomic Molecules II

  John C. Morrison, Kyle Steffen, Blake Pantoja, Asha Nagaiya, Jacek Kobus & Thomas Ericsson

  2018-04-03

  41271 3262 Pages:632-647

• PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

  Hailong Sheng, Chao Yang

  2022-10-28

  47021 3293 Pages:980-1006

• Bi-Orthogonal fPINN: A Physics-Informed Neural Network Method for Solving Time-Dependent Stochastic Fractional PDEs

  Lei Ma, Rongxin Li, Fanhai Zeng, Ling Guo, George Em Karniadakis

  2023-11-08

  31843 2797 Pages:1133-1176

• A GPU-Accelerated Cartesian Grid Method for the Heat, Wave and Schrödinger Equations on Irregular Domains

  Liwei Tan, Minsheng Huang, Wenjun Ying

  2024-09-06

  20108 1535 Pages:485-520

• Capturing Vertical Information in Radially Symmetric Flow Using Hyperbolic Shallow Water Moment Equations

  Rik Verbiest, Julian Koellermeier

  2025-09-02

  10219 549 Pages:810-848

• Multi-Valued Solution and Level Set Methods in Computational High Frequency Wave Propagation

  H. Liu, S. Osher & R. Tsai

  2006-01-01

  39506 3837 Pages:765-804

• AFEPack: A General-Purpose C++ Library for Numerical Solutions of Partial Differential Equations

  Zhenning Cai, Yun Chen, Yana Di, Guanghui Hu, Ruo Li, Wenbin Liu, Heyu Wang, Fanyi Yang, Chengbao Yao, Hongfei Zhan

  2024-07-29

  25222 2125 Pages:274-318

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  3808 139 Pages:356-386

• Fast Solver for the Local Discontinuous Galerkin Discretization of the KdV Type Equations

  Ruihan Guo & Yan Xu

  2020-07-30

  40305 3095 Pages:424-457

• On the Gauss Runge-Kutta and Method of Lines Transpose for Initial-Boundary Value Parabolic PDEs

  Bo Zhang, Dangxing Chen & Jingfang Huang

  2020-07-31

  42734 3244 Pages:1221-1240

• Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees

  Zhen Li, Zuoqiang Shi, Jian Sun

  2019-10-31

  42172 4227 Pages:228-258

• A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

  Dexuan Xie & Hans W. Volkmer

  2013-01-05

  40891 4364 Pages:174-194

• Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method

  T. Utsumi, T. Aoki, J. Koga & M. Yamagiwa

  2018-03-24

  39147 4124 Pages:261-275

• Adaptive Basis-Inspired Deep Neural Network for Solving Partial Differential Equations with Localized Features

  Ke Li, Yaqin Zhang, Yunqing Huang, Chenyue Xie, Xueshuang Xiang

  2025-09-18

  4374 321 Pages:1453-1497

• Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

  Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis

  2025-08-23

  6514 584 Pages:603-629

• Construction of the Local Structure-Preserving Algorithms for the General Multi-Symplectic Hamiltonian System

  Jialing Wang, Yushun Wang, Dong Liang

  2020-07-30

  44728 3715 Pages:828-860

• A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography

  Alia Al-Ghosoun, Ashraf S. Osman, Mohammed Seaid

  2021-02-25

  44732 3204 Pages:1095-1124

• A Weighted Runge-Kutta Method with Weak Numerical Dispersion for Solving Wave Equations

  Shan Chen, Dinghui Yang & Xiaoying Deng

  2010-07-01

  38996 4416 Pages:1027-1048

• Local Discontinuous Galerkin Method for Nonlinear BSPDEs of Neumann Boundary Conditions with Deep Backward Dynamic Programming Time-Marching

  Yixiang Dai, Yunzhang Li, Jing Zhang

  2026-01-18

  237 46 Pages:1299-1331

• The Discrete Orthogonal Polynomial Least Squares Method for Approximation and Solving Partial Differential Equations

  Anne Gelb, Rodrigo B. Platte & W. Steven Rosenthal

  2008-03-01

  39772 4363 Pages:734-758

• Numerical Simulations for Full History Recursive Multilevel Picard Approximations for Systems of High-Dimensional Partial Differential Equations

  Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler, Arnulf Jentzen, Philippe von Wurstemberger

  2020-11-18

  64386 3357 Pages:2109-2138

• Long-Time Integration of Nonlinear Wave Equations with Neural Operators

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  242 59 Pages:1137-1163

• A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations

  K. B. Nakshatrala, H. Nagarajan & M. Shabouei

  2018-04-03

  40388 4661 Pages:53-93

• On Single Distribution Lattice Boltzmann Schemes for the Approximation of Navier Stokes Equations

  François Dubois, Pierre Lallemand

  2023-10-07

  34560 2707 Pages:613-671

• Quantum Implementation of Numerical Methods for Convection-Diffusion Equations: Toward Computational Fluid Dynamics

  Bofeng Liu, Lixing Zhu, Zixuan Yang, Guowei He

  2023-03-13

  41178 3454 Pages:425-451

• Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations

  Stephan Gerster, Michael Herty

  2020-07-30

  48240 5718 Pages:639-671 Open-access

• The Unified Coordinate System in Computational Fluid Dynamics

  W. H. Hui

  2007-02-01

  39136 4144 Pages:577-610