Search Results

• 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

• Multiquadric Finite Difference (MQ-FD) Method and Its Application

  Yong Yuan Shan, Shu Chang, Ning Qin

  2018-08-10

  DOI:10.4208/aamm.09-m0942

  41705 4264 pp. 615-638

• A Fast Cascadic Multigrid Method for Direct Finite Difference Discretizations of 3D Biharmonic Equations on Rectangular Domains

  Kejia Pan, Pengde Wang, Jinxuan Wang, Xiaoxin Wu

  2026-02-01

  DOI:10.4208/aamm.OA-2023-0319

  5305 476 pp. 170-188

• 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

• 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

• Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation

  Na Zhang, Weihua Deng, Yujiang Wu

  2012-04-01

  DOI:10.4208/aamm.10-m1210

  42650 4733 pp. 496-518

• Collocation Methods for Hyperbolic Partial Differential Equations with Singular Sources

  Jae-Hun Jung, Wai Sun Don

  2021-07-01

  DOI:10.4208/aamm.09-m09S10

  41818 4266 pp. 769-780

• A Novel Discretization Method for Semilinear Reaction-Diffusion Equation

  Luoping Chen, Yanping Chen

  2018-09-17

  DOI:10.4208/aamm.OA-2017-0011

  44666 3204 pp. 409-423

• Cell-Average Based Neural Network Method for Hunter-Saxton Equations

  Chunjie Zhang, Changxin Qiu, Xiaofang Zhou, Xiaoming He

  2024-05-14

  DOI:10.4208/aamm.OA-2022-0278

  26596 2500 pp. 833-859

• A Multi-Dimensional Shock-Capturing Limiter for High-Order Least Square-Based Finite Difference-Finite Volume Method on Unstructured Grids

  Yangyang Liu, Liming Yang, Chang Shu, Huangwei Zhang

  2020-12-21

  DOI:10.4208/aamm.OA-2020-0255

  47078 3352 pp. 671-700

• A Characteristics-Mixed Volume Element Method for the Displacement Problem of Enhanced Oil Recovery

  Yirang Yuan, Aijie Cheng, Changfeng Li, Tongjun Sun, Qing Yang

  2019-06-24

  DOI:10.4208/aamm.OA-2018-0205

  45637 3298 pp. 1084-1113

• A Spectral Split-Step Padé Method for Guided Wave Propagation

  Daniel Walsken, Pavel Petrov, Matthias Ehrhardt

  2026-01-30

  DOI:10.4208/aamm.OA-2025-0179

  998 71 pp. 1602-1615

• Fourth-Order Compact Split-Step Finite Difference Method for Solving the Two- and Three-Dimensional Nonlinear Schrödinger Equations

  Rena Eskar, Xinlong Feng, Pengzhan Huang

  2018-09-17

  DOI:10.4208/aamm.OA-2017-0162

  47615 3537 pp. 879-895

• Time-Space Adaptive Finite Element Method for Nonlinear Schrödinger Equation

  Yaoyao Chen, Ying Liu, Hao Wang

  2024-12-02

  DOI:10.4208/aamm.OA-2023-0071

  14418 1215 pp. 207-223

• An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion Equations on Evolving Interfaces

  Weidong Shi, Jianjun Xu, Shi Shu

  2021-07-01

  DOI:10.4208/aamm.OA-2016-0052

  42921 3883 pp. 1364-1382

• The Second-Order Mass-Conservative Characteristic Finite Difference Method for Sobolev Equation with Convection Term

  Kai Fu, Zhaohui Liu, Jiansong Zhang

  2026-06-01

  DOI:10.4208/aamm.OA-2024-0154

  4275 103 pp. 947-960

• Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow

  Wai-Sun Don, Antonio de Gregorio, Jean-Piero Suarez, Gustaaf B. Jacobs

  2021-07-01

  DOI:10.4208/aamm.12-12S03

  43489 4425 pp. 719-736

• A Mass-Preserving Characteristic Finite Difference Method for Miscible Displacement Problem

  Jiansong Zhang, Yue Yu, Rong Qin, Zhaohui Liu

  2023-12-21

  DOI:10.4208/aamm.OA-2022-0060

  26134 2371 pp. 164-180

• A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

  Zhendong Luo

  2014-06-01

  DOI:10.4208/aamm.2013.m83

  42994 4483 pp. 615-636

• A Splitting Method for the Degasperis-Procesi Equation Using an Optimized WENO Scheme and the Fourier Pseudospectral Method

  Yunrui Guo, Wenjing Yang, Hong Zhang, Ji Wang, Songhe Song

  2019-01-04

  DOI:10.4208/aamm.OA-2018-0054

  47665 5220 pp. 53-71

• A Matrix-Vector Operation-Based Numerical Solution Method for Linear $m$-th Order Ordinary Differential Equations: Application to Engineering Problems

  M. Aminbaghai, M. Dorn, J. Eberhardsteiner, B. Pichler

  2013-05-01

  DOI:10.4208/aamm.12-m1211

  42068 4814 pp. 269-308

• Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative

  N. H. Sweilam, M. M. Abou Hasan

  2018-05-05

  DOI:10.4208/aamm.2015.m1312

  42503 2986 pp. 990-1011

• Modelling and Numerical Valuation of Power Derivatives in Energy Markets

  Mai Huong Nguyen, Matthias Ehrhardt

  2012-04-01

  DOI:10.4208/aamm.10-m1133

  41360 5192 pp. 259-293 Open Access

• A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model

  Dingwen Deng, Ruyu Zhang

  2024-02-29

  DOI:10.4208/aamm.OA-2022-0202

  27663 2890 pp. 608-635

• Effect of Nonuniform Grids on High-Order Finite Difference Method

  Dan Xu, Xiaogang Deng, Yaming Chen, Guangxue Wang, Yidao Dong

  2018-05-05

  DOI:10.4208/aamm.2016.m1477

  41041 2928 pp. 1012-1034

• Two Novel Space-Time Polynomial Particular Solutions Methods for the Time-Dependent Schrödinger Equation

  Yanhua Cao, Song Luo

  2025-09-29

  DOI:10.4208/aamm.OA-2023-0217

  7306 361 pp. 1789-1812

• 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