Search Results

• High-Order Finite Difference Schemes Based on Symmetric Conservative Metric Method: Decomposition, Geometric Meaning and Connection with Finite Volume Schemes

  Xiaogang Deng, Huajun Zhu, Yaobing Min, Huayong Liu, Meiliang Mao, Guangxue Wang

  2020-01-17

  DOI:10.4208/aamm.OA-2017-0243

  49444 3429 pp. 436-479

• A Class of Robust Low Dissipation Nested Multi-Resolution WENO Schemes for Solving Hyperbolic Conservation Laws

  Zhenming Wang, Jun Zhu, Yuchen Yang, Linlin Tian, Ning Zhao

  2021-06-08

  DOI:10.4208/aamm.OA-2020-0223

  46260 3247 pp. 1064-1095

• A Study of Fifth-Order WENO Reconstruction for Genuinely Two-Dimensional Convection-Pressure Flux Split Riemann Solver

  Shide Tan, Haizhuan Yuan, Lijun Hu

  2024-11-01

  DOI:10.4208/aamm.OA-2022-0299

  16752 1558 pp. 1297-1327

• Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles

  Xiaofan Zhang, Shoufu Tian, Jinjie Yang

  2022-04-11

  DOI:10.4208/aamm.OA-2020-0369

  45355 3681 pp. 893-913

• A Modified Hybrid High-Order Essentially Non-Oscillatory Compact Difference Scheme for Nonlinear Degenerate Parabolic Equations

  Xiaohua Zhang, Shengfeng Wang

  2026-04-01

  DOI:10.4208/aamm.OA-2023-0261

  5091 270 pp. 482-518

• Improvements to Enhance Robustness of Third-Order Scale-Independent WENO-Z Schemes

  Qin Li, Pan Yan, Xiao Huang, Yihui Weng, Yancheng You, Yi Duan

  2024-12-31

  DOI:10.4208/aamm.OA-2023-0244

  13654 1337 pp. 373-406

• A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations

  Zhongguo Zhou, Dong Liang

  2018-05-05

  DOI:10.4208/aamm.2015.m1049

  42363 3101 pp. 795-817

• An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces

  Kai Jiang, Xin Wang, Jianggang Liu, Huayi Wei

  2024-12-02

  DOI:10.4208/aamm.OA-2023-0061

  14758 1288 pp. 123-147

• High-Order Numerical Approximation and Error Estimation for Fourth-Order Equation in Complex Cylindrical Domain

  Xuenan Zhao, Jing An, Juan Zhang

  2026-08-01

  DOI:10.4208/aamm.OA-2024-0276

  1033 83 pp. 1189-1209

• A Hybrided Trapezoidal-Difference Scheme for Nonlinear Time-Fractional Fourth-Order Advection-Dispersion Equation Based on Chebyshev Spectral Collocation Method

  Shichao Yi, Hongguang Sun

  2019-01-04

  DOI:10.4208/aamm.OA-2018-0045

  46708 4547 pp. 197-215

• Corrected Linear-Galerkin Schemes to Preserve Second-Order Accuracy for Cell-Centered Unstructured Finite Volume Methods

  Lingfa Kong, Yidao Dong, Wei Liu

  2024-07-22

  DOI:10.4208/aamm.OA-2023-0113

  31751 2455 pp. 1056-1103

• A New Fifth-Order Finite Volume Central WENO Scheme for Hyperbolic Conservation Laws on Staggered Meshes

  Shengzhu Cui, Zhanjing Tao, Jun Zhu

  2022-06-13

  DOI:10.4208/aamm.OA-2021-0095

  43647 3621 pp. 1059-1086

• A Combination of High-Order Compact Finite Difference Schemes and a Splitting Method that Preserves Accuracy for the Multi-Dimensional Burgers' Equation

  Shengfeng Wang, Xiaohua Zhang, Julian Koellermeier, Daobin Ji

  2021-06-08

  DOI:10.4208/aamm.OA-2020-0277

  45318 3140 pp. 1261-1292

• A Fourth Order WENO Scheme for Hyperbolic Conservation Laws

  Xiaohan Cheng, Jianhu Feng, Supei Zheng

  2020-06-01

  DOI:10.4208/aamm.OA-2019-0097

  52700 3608 pp. 992-1007

• Solving Fourth-Order PDEs Using the LMAPS

  Cheng Deng, Hui Zheng, Yan Shi, C. S. Chen

  2020-06-01

  DOI:10.4208/aamm.OA-2019-0216

  50895 3404 pp. 920-939

• High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics

  Junming Duan, Huazhong Tang

  2020-03-06

  DOI:10.4208/aamm.OA-2019-0124

  142377 5909 pp. 1-29

• A Novel Temporal Two-Grid Compact Finite Difference Scheme for the Viscous Burgers’ Equation

  Xiangyi Peng, Wenlin Qiu, Jiangxing Wang, Lina Ma

  2024-11-01

  DOI:10.4208/aamm.OA-2022-0302

  16176 1523 pp. 1358-1380

• A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics

  Eric Ngondiep

  2025-03-14

  DOI:10.4208/aamm.OA-2022-0320

  11395 868 pp. 956-988

• Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions

  Jia-Le Li, Wai-Sun Don, Cai-Feng Wang, Bao-Shan Wang

  2025-03-14

  DOI:10.4208/aamm.OA-2023-0306

  11682 907 pp. 804-839

• The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation

  Dan Qin, Kai Fu, Dong Liang

  2025-03-14

  DOI:10.4208/aamm.OA-2023-0173

  11582 918 pp. 732-757

• Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations

  Xiaojun Zhou, Chuanju Xu

  2018-08-04

  DOI:10.4208/aamm.2015.m1054

  42367 3151 pp. 574-595

• A Straightforward $hp$-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods

  Hongqiang Lu, Qiang Sun

  2014-06-01

  DOI:10.4208/aamm.2013.m-s1

  44756 5038 pp. 135-144

• Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System

  Seakweng Vong, Zhibo Wang

  2014-06-01

  DOI:10.4208/aamm.2014.4.s1

  44461 4686 pp. 419-435

• Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations

  Quan Zhou, Yabing Sun

  2021-11-17

  DOI:10.4208/aamm.OA-2020-0133

  50181 4076 pp. 1293-1317

• A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations

  Xiaogang Li, Guodong Li, Yongbin Ge

  2020-10-20

  DOI:10.4208/aamm.OA-2019-0155

  51294 4914 pp. 58-82

• $(1+s)$-Order Convergence Analysis of Weak Galerkin Finite Element Methods for Second Order Elliptic Equations

  Yiying Wang, Yongkui Zou, Shimin Chai

  2020-12-21

  DOI:10.4208/aamm.OA-2020-0020

  47914 3259 pp. 554-568

• Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach

  Huimin Ma, Pengzhan Huang

  2026-02-01

  DOI:10.4208/aamm.OA-2023-0325

  5380 468 pp. 109-133