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• Fourth-Order Splitting Methods for Time-Dependant Differential Equations

  Jürgen Geiser

  2008-01-01

  39151 3532 Pages:321-339

• Effect of Space Dimensions on Equilibrium Solutions of Cahn-Hilliard and Conservative Allen-Cahn Equations

  Hyun Geun Lee, Junxiang Yang, Junseok Kim, Jintae Park

  2020-03-16

  45565 2863 Pages:644-664

• 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

  40114 3138 Pages:298-322

• PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations

  Ruisong Gao, Yufeng Wang, Min Yang, Chuanjun Chen

  2023-11-07

  27792 2414 Pages:931-953

• ODE-Based Multistep Schemes for Backward Stochastic Differential Equations

  Shuixin Fang, Weidong Zhao

  2023-11-07

  28343 2410 Pages:1053-1086

• A Fitted Numerov Method for Singularly Perturbed Parabolic Partial Differential Equation with a Small Negative Shift Arising in Control Theory

  R. Nageshwar Rao & P. Pramod Chakravarthy

  2014-07-01

  41580 4450 Pages:23-40

• 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

  53366 3099 Pages:881-907

• Sparse Deep Neural Network for Nonlinear Partial Differential Equations

  Yuesheng Xu, Taishan Zeng

  2023-01-13

  34437 3135 Pages:58-78

• Adaptive Dimensionality-Reduction for Time-Stepping in Differential and Partial Differential Equations

  Xing Fu & J. Nathan Kutz

  2017-11-02

  39316 2657 Pages:872-894

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

  Jiang Yang, Quanhui Zhu

  2022-02-09

  47124 4540 Pages:42-67

• A Numerical Approximation Structured by Mixed Finite Element and Upwind Fractional Step Difference for Semiconductor Device with Heat Conduction and Its Numerical Analysis

  Yirang Yuan, Qing Yang, Changfeng Li & Tongjun Sun

  2017-10-01

  39156 2676 Pages:541-561

• Numerical Approximation to a Stochastic Parabolic PDE with Weak Galerkin Method

  Hongze Zhu, Yongkui Zou, Shimin Chai & Chenguang Zhou

  2018-09-17

  41723 2742 Pages:604-617

• A Novel Semi-Analytical Multiple Invariants-Preserving Integrator for Conservative PDEs

  Wei Shi, Bin Wang, Kai Liu

  2026-01-21

  37 62

• A Review of Unified a Posteriori Finite Element Error Control

  C. Carstensen, M. Eigel, R. H. W. Hoppe & C. Löbhard

  2012-05-01

  44992 4425 Pages:509-558 Open-access

• A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints

  Hao Liu, Shingyu Leung

  2020-03-16

  43916 2943 Pages:620-643

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

  Jichang Xiao, Xiaoqun Wang

  2024-12-11

  11943 1346 Pages:996-1017

• Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type

  Yanzhao Cao & Li Yin

  2011-04-01

  40497 4496 Pages:38-52

• Evaluation Finite Moment Log-Stable Option Pricing by a Spectral Method

  Xu Guo & Leevan Ling

  2018-09-17

  51160 2856 Pages:437-452

• A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations

  Buyun Chen, Dongdong He & Kejia Pan

  2018-09-17

  42207 2896 Pages:299-320

• Error Analysis of the Mixed Residual Method for Elliptic Equations

  Kai Gu, Peng Fang, Zhiwei Sun, Rui Du

  2024-05-11

  21043 1712 Pages:534-554

• Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation

  G.N. Milstein, M.V. Tretyakov

  2020-10-09

  48918 3878 Pages:1-30

• 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

  44410 2767 Pages:497-515

• Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks

  Jingrun Chen, Rui Du, Panchi Li, Liyao Lyu

  2021-01-26

  46361 2749 Pages:377-404

• Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations

  Róisín Hill, Niall Madden

  2021-06-02

  61152 3245 Pages:559-588

• Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients

  Xu Yang, Weidong Zhao

  2021-09-10

  45699 2757 Pages:1085-1109

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

  Fengjiang Fu, Xiaoqun Wang

  2023-08-29

  28404 2513 Pages:668-700

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

  Xia Ji & Huazhong Tang

  2012-05-01

  41683 3649 Pages:333-358