Search Results

• A Local Deep Learning Method for Solving High Order Partial Differential Equations

  Jiang Yang, Quanhui Zhu

  2022-02-09

  DOI:10.4208/nmtma.OA-2021-0035

  47238 4622 pp. 42-67

• Error Analysis for Empirical Risk Minimization over Clipped ReLU Networks in Solving Linear Kolmogorov Partial Differential Equations

  Jichang Xiao, Xiaoqun Wang

  2024-12-11

  DOI:10.4208/nmtma.OA-2024-0026

  12055 1377 pp. 996-1017

• R-Adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-Adaptive Strategy

  Yameng Zhu, Jingrun Chen, Weibing Deng

  2025-04-06

  DOI:10.4208/nmtma.OA-2024-0124

  7155 774 pp. 31-65

• A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs

  Yong Yu, Gang Chen, Liangya Pi, Yangwen Zhang

  2020-10-09

  DOI:10.4208/nmtma.OA-2019-0190

  48608 3642 pp. 144-175

• FDMs for the PDEs of Option Pricing Under DEV Models with Counterparty Risk

  Jingtang Ma, Yong Chen, Taoshun He, Zhijun Tan

  2019-10-12

  DOI:10.4208/nmtma.OA-2018-0126

  44376 2634 pp. 1246-1265

• On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs

  Rui Sheng, Jerry Zhijian Yang, Cheng Yuan

  2025-05-16

  DOI:10.4208/nmtma.OA-2024-0100

  7646 578 pp. 487-520

• Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients

  Xinliang Liu, Lei Zhang, Shengxin Zhu

  2021-09-10

  DOI:10.4208/nmtma.OA-2021-0100

  48030 2785 pp. 862-892

• An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations

  Shuyan Shi, Ding Liu, Ruirui Ji, Yuchao Han

  2023-04-10

  DOI:10.4208/nmtma.OA-2022-0063

  40305 3188 pp. 298-322

• Efficient Chebyshev Spectral Method for Solving Linear Elliptic PDEs Using Quasi-Inverse Technique

  Fei Liu, Xingde Ye, Xinghua Wang

  2011-04-01

  DOI:10.4208/nmtma.2011.42s.5

  40309 3838 pp. 197-215

• Mesh Spacing Estimates and Efficiency Considerations for Moving Mesh Systems

  Joan Remski

  2016-09-01

  DOI:10.4208/nmtma.2016.m1508

  39681 2842 pp. 432-450

• An Adaptive Complex Collocation Method for Solving Linear Elliptic PDEs in Regular Convex Polygons Based on the Unified Transform

  E-N G. Grylonakis, C. K. Filelis-Papadopoulos, G. A. Gravvanis, A. S. Fokas

  2018-12-17

  DOI:10.4208/nmtma.OA-2018-0017

  43254 2973 pp. 348-369

• High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models

  Jingtang Ma, Han Wang, Zhiqiang Zhou, Zhijun Tan

  2020-03-09

  DOI:10.4208/nmtma.OA-2019-0119

  44521 2803 pp. 497-515

• Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations

  Róisín Hill, Niall Madden

  2021-06-02

  DOI:10.4208/nmtma.OA-2020-0187

  61270 3275 pp. 559-588

• Numerical Continuation and Bifurcation for Differential Geometric PDEs

  Alexander Meiners, Hannes Uecker

  2024-08-30

  DOI:10.4208/nmtma.OA-2024-0005

  22723 1549 pp. 555-606

• MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling

  Xiaodong Feng, Yue Qian, Wanfang Shen

  2023-08-29

  DOI:10.4208/nmtma.OA-2022-0201

  28455 2484 pp. 769-791

• Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations

  Fengjiang Fu, Xiaoqun Wang

  2023-08-29

  DOI:10.4208/nmtma.OA-2022-0166

  28533 2542 pp. 668-700

• Newton-Multigrid for Biological Reaction-Diffusion Problems with Random Coefficients

  Eveline Rosseel, Nico Scheerlinck, Stefan Vandewalle

  2012-05-01

  DOI:10.4208/nmtma.2011.m12si04

  40928 4599 pp. 62-84 Open Access

• High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations

  Xia Ji, Huazhong Tang

  2012-05-01

  DOI:10.4208/nmtma.2012.m1107

  41801 3686 pp. 333-358

• pde2path - A Matlab Package for Continuation and Bifurcation in 2D Elliptic Systems

  Hannes Uecker, Daniel Wetzel, Jens D. M. Rademacher

  2014-07-01

  DOI:10.4208/nmtma.2014.1231nm

  47748 5805 pp. 58-106

• A Splitting Scheme for the Numerical Solution of the KWC System

  R. H. W. Hoppe, J. J. Winkle

  2019-04-22

  DOI:10.4208/nmtma.OA-2018-0050

  54523 3039 pp. 661-680

• A Continuous-Stage Modified Leap-Frog Scheme for High-Dimensional Semi-Linear Hamiltonian Wave Equations

  Bin Wang, Xinyuan Wu, Yonglei Fang

  2020-03-16

  DOI:10.4208/nmtma.OA-2019-0115

  44289 2736 pp. 814-844

• Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part I: Concepts and Fundamentals

  M. Esmaeilzadeh, R.M. Barron, R. Balachandar

  2020-12-02

  DOI:10.4208/nmtma.OA-2019-0143

  53489 3136 pp. 881-907

• An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems

  Changjuan Zhang, Zhilin Li, Xingye Yue

  2021-06-02

  DOI:10.4208/nmtma.OA-2020-0112

  47260 2834 pp. 773-796

• A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations

  Xian-Ming Gu, Yong-Liang Zhao, Xi-Le Zhao, Bruno Carpentieri, Yu-Yun Huang

  2021-09-10

  DOI:10.4208/nmtma.OA-2020-0020

  49331 2796 pp. 893-919

• The Method of Fundamental Solutions for Optical Fluorescence Tomography

  Andreas Karageorghis, Daniel Lesnic

  2026-01-14

  DOI:10.4208/nmtma.OA-2025-0101

  450 177 pp. 219-239

• Weakly Admissible Meshes and Discrete Extremal Sets

  Len Bos, Stefano De Marchi, Alvise Sommariva, Marco Vianello

  2011-04-01

  DOI:10.4208/nmtma.2011.m1003

  40064 4263 pp. 1-12

• An Efficient Particle-Field Algorithm with Neural Interpolation Based on a Parabolic-Hyperbolic Chemotaxis System in 3D

  Jongwon David Kim, Jack Xin

  2026-04-16

  DOI:10.4208/nmtma.OA-2025-0127

  19 12