On the selection of a good value of shape parameter in solving time-dependent partial differential equations using RBF approximation method

被引：64

作者：

Uddin, Marjan ^{[1
]}

机构：

[1] Univ Engn & Technol, Dept Basic Sci, Peshawar, Pakistan

来源：

APPLIED MATHEMATICAL MODELLING | 2014年 / 38卷 / 01期

关键词：

Kernel functions; Partial differential equations; Cross validation; Shape parameter; RADIAL BASIS FUNCTIONS; FUNCTION COLLOCATION METHODS; MESH-FREE METHOD; NUMERICAL-SOLUTION; SCATTERED DATA; INTERPOLATION; SCHEME; MULTIQUADRICS;

D O I：

10.1016/j.apm.2013.05.060

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Radial basis function method is an effective tool for solving differential equations in engineering and sciences. Many radial basis functions contain a shape parameter c which is directly connected to the accuracy of the method. Rippa [1] proposed an algorithm for selecting good value of shape parameter c in RBF-interpolation. Based on this idea, we extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：135 / 144

页数：10

共 47 条

[1] Optimal constant shape parameter for multiquadric based RBF-FD method
Bayona, Victor
Moscoso, Miguel
Kindelan, Manuel
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (19) : 7384 - 7399
[2] An analysis of the linear advection-diffusion equation using mesh-free and mesh-dependent methods
Boztosun, I
Charafi, A
[J]. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2002, 26 (10) : 889 - 895
[3] A mesh-free method for linear diffusion equations
Chen, CS
Rashed, YF
Golberg, MA
[J]. NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, 1998, 33 (04) : 469 - 486
[4] Radial basis functions for solving near singular Poisson problems
Chen, CS
Kuhn, G
Li, J
Mishuris, G
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 2003, 19 (05): : 333 - 347
[5] Multilevel compact radial functions based computational schemes for some elliptic problems
Chen, CS
Ganesh, M
Golberg, MA
Cheng, AHD
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (3-5) : 359 - 378
[6] Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation
Chinchapatnam, PP
Djidjeli, K
Nair, PB
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (19-22) : 2432 - 2453
[7] Numerical solutions of KdV equation using radial basis functions
Dag, Idris
Dereli, Yilmaz
[J]. APPLIED MATHEMATICAL MODELLING, 2008, 32 (04) : 535 - 546
[8] Numerical solution of RLW equation using radial basis functions
Dag, Idris
Dereli, Yilmaz
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (01) : 63 - 76
[9] A numerical method for KdV equation using collocation and radial basis functions
Dehghan, Mehdi
Shokri, Ali
[J]. NONLINEAR DYNAMICS, 2007, 50 (1-2) : 111 - 120
[10] Radial basis functions method for numerical solution of the modified equal width equation
Dereli, Yilmaz
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (07) : 1569 - 1577

← 1 2 3 4 5 →