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

  DOI:10.4208/cicp.101114.170615a

  41360 3284 pp. 632-647

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

  Hailong Sheng, Chao Yang

  2022-10-28

  DOI:10.4208/cicp.OA-2022-0114

  47150 3352 pp. 980-1006

• Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Lévy Equations

  Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi

  2026-04-10

  DOI:10.4208/cicp.OA-2024-0201

  170 55 pp. 1-26

• 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

  DOI:10.4208/cicp.OA-2023-0075

  32040 2870 pp. 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

  DOI:10.4208/cicp.OA-2023-0025

  20233 1592 pp. 485-520

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

  Rik Verbiest, Julian Koellermeier

  2025-09-02

  DOI:10.4208/cicp.OA-2024-0047

  10365 572 pp. 810-848

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

  Hailiang Liu, Stanley Osher, Richard Tsai

  2006-01-01

  39604 3888 pp. 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

  DOI:10.4208/cicp.OA-2024-0027

  25367 2322 pp. 274-318

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  DOI:10.4208/cicp.OA-2025-0082

  4126 195 pp. 356-386

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

  Ruihan Guo, Yan Xu

  2020-07-30

  DOI:10.4208/cicp.210114.080814a

  40380 3124 pp. 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

  DOI:10.4208/cicp.2018.hh80.09

  42831 3287 pp. 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

  DOI:10.4208/cicp.111015.250716a

  42282 4279 pp. 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

  DOI:10.4208/cicp.170811.211011s

  40984 4426 pp. 174-194

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

  Takayuki Utsumi, Takayuki Aoki, James Koga, Mitsuru Yamagiwa

  2018-03-24

  39240 4159 pp. 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

  DOI:10.4208/cicp.OA-2024-0263

  4572 375 pp. 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

  DOI:10.4208/cicp.OA-2024-0040

  6671 631 pp. 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

  DOI:10.4208/cicp.OA-2018-0160

  44852 3769 pp. 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

  DOI:10.4208/cicp.OA-2020-0098

  44831 3229 pp. 1095-1124

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

  Shan Chen, Dinghui Yang, Xiaoying Deng

  2010-07-01

  DOI:10.4208/cicp.2009.09.088

  39090 4438 pp. 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

  DOI:10.4208/cicp.OA-2024-0296

  785 122 pp. 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

  39868 4402 pp. 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

  DOI:10.4208/cicp.OA-2020-0130

  64587 3389 pp. 2109-2138

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

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  DOI:10.4208/cicp.OA-2024-0274

  792 146 pp. 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

  DOI:10.4208/cicp.180615.280815a

  40479 4767 pp. 53-93

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

  François Dubois, Pierre Lallemand

  2023-10-07

  DOI:10.4208/cicp.OA-2022-0185

  34708 2747 pp. 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

  DOI:10.4208/cicp.OA-2022-0081

  41322 3496 pp. 425-451

• Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations

  Stephan Gerster, Michael Herty

  2020-07-30

  DOI:10.4208/cicp.OA-2019-0047

  48362 5794 pp. 639-671 Open Access