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• Mixed Interior Penalty Discontinuous Galerkin Methods for One-Dimensional Fully Nonlinear Second Order Elliptic and Parabolic Equations

  Xiaobing Feng & Thomas Lewis

  2018-08-22

  36870 4874 Pages:107-135 Open-access

• Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

  Genming Bai, Ujjwal Koley, Siddhartha Mishra, Roberto Molinaro

  2021-11-19

  41374 3767 Pages:816-847

• Semi-Implicit Spectral Deferred Correction Methods Based on Second-Order Time Integration Schemes for Nonlinear PDEs

  Ruihan Guo, Yan Xu

  2023-12-01

  31479 2997 Pages:111-133

• Alternating Direction Implicit Schemes for the Two-Dimensional Time Fractional Nonlinear Super-Diffusion Equations

  Jianfei Huang, Yue Zhao, Sadia Arshad, Kuangying Li, Yifa Tang

  2019-04-29

  42067 3002 Pages:297-315

• The Mortar Element Method for a Nonlinear Biharmonic Equation

  Zhong-Ci Shi & Xue-Jun Xu

  2005-10-02

  33622 3411 Pages:537-560

• A Neuron-Wise Subspace Correction Method for the Finite Neuron Method

  Jongho Park, Jinchao Xu, Xiaofeng Xu

  2025-10-30

  4279 252 Pages:1488-1511

• A Linearly-Fitted Conservative (Dissipative) Scheme for Efficiently Solving Conservative (Dissipative) Nonlinear Wave PDEs

  Kai Liu, Xinyuan Wu, Wei Shi

  2021-07-01

  39843 3707 Pages:780-800

• Uniform Error Bounds of an Energy-Preserving Exponential Wave Integrator Fourier Pseudo-Spectral Method for the Nonlinear Schrödinger Equation with Wave Operator and Weak Nonlinearity

  Jiyong Li

  2024-11-19

  13946 1106 Pages:280-314

• A Reduced Order Schwarz Method for Nonlinear Multiscale Elliptic Equations Based on Two-Layer Neural Networks

  Shi Chen, Zhiyan Ding, Qin Li, Stephen J. Wright

  2024-01-16

  25808 2144 Pages:570-596

• A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs

  Yayun Fu, Dongdong Hu, Wenjun Cai, Yushun Wang

  2024-04-09

  26500 1997 Pages:1063-1079

• Quantum Simulation of a Class of Highly-Oscillatory Transport Equations via Schrödingerisation

  Anjiao Gu, Shi Jin

  2025-09-28

  4787 412 Pages:1092-1117

• High Resolution Schemes for Conservation Laws and Convection-Diffusion Equations with Varying Time and Space Grids

  Hua-Zhong Tang & Gerald Warnecke

  2006-04-02

  31962 3380 Pages:121-140

• High-Order Local Absorbing Boundary Conditions for Heat Equation in Unbounded Domains

  Xiaonan Wu & Jiwei Zhang

  2018-08-22

  33900 3991 Pages:74-90

• Numerical Analysis of Nonstationary Thermistor Problem

  Xing-Ye Yue

  1994-12-01

  33431 3640 Pages:213-223