A radial basis function method for fractional Darboux problems

被引：9
|
作者：
Chandhini, G. [1 ]
Prashanthi, K. S. [1 ]
Vijesh, V. Antony [2 ]
机构：
[1] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Surathkal 575025, India
[2] Indian Inst Technol Indore, Sch Basic Sci, Indore 452017, Madhya Pradesh, India
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2018年 / 86卷
关键词：
Fractional Darboux problem; Radial basis function; Collocation; Successive approximation; Gauss-Jacobi quadrature; PARTIAL-DIFFERENTIAL-EQUATIONS; OPTIMAL SHAPE-PARAMETERS; INITIAL-VALUE-PROBLEMS; NUMERICAL-SOLUTION; GOURSAT PROBLEM; DIFFUSION-EQUATIONS; APPROXIMATION; ORDER; INTERPOLATION; COLLOCATION;
D O I：
10.1016/j.enganabound.2017.10.001
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, a radial basis function (RBF) collocation known as Kansa's method has been extended to solve fractional Darboux problems. The fractional derivatives are described in the Caputo sense. Integration of radial functions that appears due to fractional derivatives have been dealt using Gauss-Jacobi quadrature method. The equation has been linearized using successive approximation. A few test problems have been solved and compared with available solutions. The effect of RBF shape parameter on accuracy and convergence has also been discussed. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1 / 18
页数：18
相关论文
共 50 条
  • [31] Kansa radial basis function method with fictitious centres for solving nonlinear boundary value problems
    Katsiamis, Andreas
    Karageorghis, Andreas
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2020, 119 : 293 - 301
  • [32] A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
    Liu, Xiao-Yan
    Karageorghis, Andreas
    Chen, C. S.
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2015, 65 (03) : 1240 - 1269
  • [33] A novel local radial basis function collocation method for multi-dimensional piezoelectric problems
    Noorizadegan, Amir
    Young, Der Liang
    Chen, Chuin-Shan
    [J]. JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, 2022, 33 (12) : 1574 - 1587
  • [34] A Local Radial Basis Function Method for High-Dimensional American Option Pricing Problems
    Company, Rafael
    Egorova, Vera N.
    Jodar, Lucas
    Soleymani, Fazlollah
    [J]. MATHEMATICAL MODELLING AND ANALYSIS, 2018, 23 (01) : 117 - 138
  • [35] Solving Helmholtz problems with the boundary element method using direct radial basis function interpolation
    Loeffler, Carlos Friedrich
    Mansur, Webe Joao
    Barcelos, Hercules de Melo
    Bulcao, Andre
    [J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2015, 61 : 218 - 225
  • [36] Topological Shape Optimization of Electromagnetic Problems using Level Set Method and Radial Basis Function
    Shim, Hokyung
    Ho, Vinh Thuy Tran
    Wang, Semyung
    Tortorelli, Daniel A.
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2008, 37 (02): : 175 - 202
  • [37] A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
    Xiao-Yan Liu
    Andreas Karageorghis
    C. S. Chen
    [J]. Journal of Scientific Computing, 2015, 65 : 1240 - 1269
  • [38] Ellipsoidal/radial basis functions neural networks enhanced with the Rvachev function method in application problems
    Varvak, Mark
    [J]. ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 2015, 38 : 111 - 121
  • [39] h-Adaptive radial basis function finite difference method for linear elasticity problems
    Balázs Tóth
    Alexander Düster
    [J]. Computational Mechanics, 2023, 71 : 433 - 452
  • [40] An operator splitting-radial basis function method for the solution of transient nonlinear Poisson problems
    Balakrishnan, K
    Sureshkumar, R
    Ramachandran, PA
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (3-5) : 289 - 304
12345