The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations

被引：24
|
作者：
Yao, Guangming [2 ]
Tsai, C. H. [2 ]
Chen, Wen [1 ]
机构：
[1] Hohai Univ, Dept Mech, Nanjing, Peoples R China
[2] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2010年 / 34卷 / 07期
关键词：
Radial basis function; MFS; MPS; Kansa's method; LEAKY AQUIFER SYSTEMS; POLYHARMONIC OPERATORS; FUNDAMENTAL-SOLUTIONS; HELMHOLTZ; PRODUCTS;
D O I：
10.1016/j.enganabound.2010.03.004
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper we apply the newly developed method of particular solutions (MPS) and one-stage method of fundamental solutions (MFS-MPS) for solving fourth-order partial differential equations. We also compare the numerical results of these two methods to the popular Kansas method. Numerical results in the 2D and the 3D show that the MFS-MPS outperformed the MPS and Kansas method. However, the MPS and Kansas method are easier in terms of implementation. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：625 / 631
页数：7
相关论文
共 50 条
  • [21] Solving differential equations with radial basis functions: multilevel methods and smoothing
    Fasshauer, GE
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 1999, 11 (2-3) : 139 - 159
  • [22] Solving differential equations with radial basis functions: multilevel methods and smoothing
    Gregory E. Fasshauer
    Advances in Computational Mathematics, 1999, 11 : 139 - 159
  • [23] On the effect of order of radial basis functions in the solution of partial differential equations
    Hutchcraft, W. Elliott
    Gordon, Richard K.
    2007 IEEE ANTENNAS AND PROPAGATION SOCIETY INTERNATIONAL SYMPOSIUM, VOLS 1-12, 2007, : 3317 - 3320
  • [24] Fourth-order partial differential equations for image inpainting
    Chen, Peiying
    Wang, Yuandi
    2008 INTERNATIONAL CONFERENCE ON AUDIO, LANGUAGE AND IMAGE PROCESSING, VOLS 1 AND 2, PROCEEDINGS, 2008, : 1713 - 1717
  • [25] Fourth-order partial differential equations for image enhancement
    Yi, Dokkyun
    Lee, Sungyun
    APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (01) : 430 - 440
  • [26] Fourth-order partial differential equations for noise removal
    You, YL
    Kaveh, M
    IEEE TRANSACTIONS ON IMAGE PROCESSING, 2000, 9 (10) : 1723 - 1730
  • [27] Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations
    M. Dirbaz
    T. Allahviranloo
    Computational and Applied Mathematics, 2019, 38
  • [28] Fuzzy multiquadric radial basis functions for solving fuzzy partial differential equations
    Dirbaz, M.
    Allahviranloo, T.
    COMPUTATIONAL & APPLIED MATHEMATICS, 2019, 38 (04):
  • [29] GREEN'S FUNCTIONS FOR THE FOURTH-ORDER DIFFERENTIAL EQUATIONS
    Bouakkaz, Ahleme
    Ardjouni, Abdelouaheb
    Khemis, Rabah
    Djoudi, Ahcene
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2019, 77 : 13 - 41
  • [30] Convergence order estimates of meshless collocation methods using radial basis functions
    Carsten Franke
    Robert Schaback
    Advances in Computational Mathematics, 1998, 8 : 381 - 399
12345