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

  Guanhang Lei, Zhen Lei, Lei Shi

  2026-01-18

  242 59 Pages:1137-1163

• Integral Regularization PINNs for Evolution Equations

  Xiaodong Feng, Haojiong Shangguan, Tao Tang, Xiaoliang Wan

  2026-02-15

  3808 139 Pages:356-386

• An Energy Conserving Local Discontinuous Galerkin Method for a Nonlinear Variational Wave Equation

  Nianyu Yi & Hailiang Liu

  2018-08-21

  46501 3244 Pages:747-772

• Direct Vlasov Solvers with High-Order Spectral Element Method

  Jin Xu, Brahim Mustapha, Peter Ostroumov & Jerry Nolen

  2010-08-01

  39511 4569 Pages:159-184

• A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

  Hector D. Ceniceros, Alexandre M. Roma, Aristeu Silveira-Neto & Millena M. Villar

  2010-08-01

  40201 4535 Pages:51-94

• Optimal Superconvergence of Energy Conserving Local Discontinuous Galerkin Methods for Wave Equations

  Waixiang Cao, Dongfang Li & Zhimin Zhang

  2018-04-08

  41342 4699 Pages:211-236

• 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 Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem

  Hong-Lin Liao, William McLean, Jiwei Zhang

  2021-05-25

  54747 3560 Pages:567-601