Search Results

• Time Integration Schemes Based on Neural Networks for Solving Partial Differential Equations on Coarse Grids

  Xinxin Yan, Zhideng Zhou, Xiaohan Cheng, Xiaolei Yang

  2024-12-02

  DOI:10.4208/cicp.OA-2023-0266

  15998 1216 pp. 1262-1306

• Quantum Simulation of the Fokker-Planck Equation via Schrödingerization

  Shi Jin, Nana Liu, Yue Yu

  2026-01-18

  DOI:10.4208/cicp.OA-2024-0097

  1060 298 pp. 969-1001

• 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

• A Splitting Method for Nonlinear Filtering Problems with Diffusive and Point Process Observations

  Fengshan Zhang, Yongkui Zou, Shimin Chai, Yanzhao Cao

  2024-10-29

  DOI:10.4208/cicp.OA-2024-0074

  17992 1206 pp. 996-1020

• Weak Collocation Regression for Inferring Stochastic Dynamics with Lévy Noise

  Liya Guo, Liwei Lu, Zhijun Zeng, Pipi Hu, Yi Zhu

  2025-05-29

  DOI:10.4208/cicp.OA-2024-0001

  9059 533 pp. 1277-1304

• Data Generation-Based Operator Learning for Solving Partial Differential Equations on Unbounded Domains

  Jihong Wang, Xin Wang, Jing Li, Bin Liu

  2025-05-29

  DOI:10.4208/cicp.OA-2023-0327

  9043 520 pp. 1383-1416

• A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases

  Juan-Chen Huang, Kun Xu, Pubing Yu

  2012-12-01

  DOI:10.4208/cicp.030511.220911a

  41044 4193 pp. 662-690

• The Hyperbolic Schrödinger Equation and the Quantum Lattice Boltzmann Approximation

  Renato Spigler

  2022-05-06

  DOI:10.4208/cicp.OA-2022-0001

  44645 3325 pp. 1341-1361

• 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

• DL-PDE: Deep-Learning Based Data-Driven Discovery of Partial Differential Equations from Discrete and Noisy Data

  Hao Xu, Haibin Chang, Dongxiao Zhang

  2021-01-13

  DOI:10.4208/cicp.OA-2020-0142

  55435 3561 pp. 698-728

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

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

  2018-09-17

  DOI:10.4208/cicp.OA-2017-0192

  46850 3342 pp. 623-634

• Curious Convergence Properties of Lattice Boltzmann Schemes for Diffusion with Acoustic Scaling

  Bruce M. Boghosian, Francois Dubois, Benjamin Graille, Pierre Lallemand, Mohamed-Mahdi Tekitek

  2020-07-31

  DOI:10.4208/cicp.OA-2016-0257

  50238 3150 pp. 1263-1278

• 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

• An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation

  Min Zhang, Juan Cheng, Weizhang Huang, Jianxian Qiu

  2020-02-23

  DOI:10.4208/cicp.OA-2018-0317

  51085 3289 pp. 1140-1173

• 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

• Multigrid Method for the Chan-Vese Model in Variational Segmentation

  Noor Badshah, Ke Chen

  2018-03-24

  38142 3903 pp. 294-316

• 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

• 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

• Recursive POD Expansion for the Advection-Diffusion-Reaction Equation

  M. Azaiez, T. Chacon Rebollo, E. Perracchione, J. M. Vega

  2018-09-17

  DOI:10.4208/cicp.OA-2017-0257

  44603 4776 pp. 1556-1578 Open Access

• Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

  M. J. Baines, M. E. Hubbard, P. K. Jimack

  2011-10-01

  DOI:10.4208/cicp.201010.040511a

  40073 5040 pp. 509-576 Open Access

• 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 Coupled High-Order Continuous and Discontinuous Galerkin Finite Element Scheme for the Davey-Stewartson System

  Jinyang Lu, Qi Tao, Yan Xu

  2025-04-27

  DOI:10.4208/cicp.OA-2022-0299

  9635 584 pp. 975-1007

• 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

• Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks (PINNs)

  Shamsulhaq Basir

  2023-06-06

  DOI:10.4208/cicp.OA-2022-0239

  41861 3031 pp. 1240-1269

• 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

• Mesh Density Functions Based on Local Bandwidth Applied to Moving Mesh Methods

  Elliott S. Wise, Ben T. Cox, Bradley E. Treeby

  2017-11-02

  DOI:10.4208/cicp.OA-2016-0246

  42861 3562 pp. 1286-1308

• Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

  F. Chinesta, E. Abisset-Chavanne, A. Ammar, E. Cueto

  2018-04-02

  DOI:10.4208/cicp.2014.m326

  38833 3012 pp. 975-1006