Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.camwa.2005.02.019
Title: Radial point interpolation collocation method (RPICM) for partial differential equations
Authors: Liu, X.
Liu, G.R. 
Tai, K.
Lam, K.Y.
Keywords: Hermite-type interpolation
Meshfree
Partial differential equations
RPICM
Issue Date: Oct-2005
Source: Liu, X., Liu, G.R., Tai, K., Lam, K.Y. (2005-10). Radial point interpolation collocation method (RPICM) for partial differential equations. Computers and Mathematics with Applications 50 (8-9) : 1425-1442. ScholarBank@NUS Repository. https://doi.org/10.1016/j.camwa.2005.02.019
Abstract: This paper presents a truly meshfree method referred to as radial point interpolation collocation method (RPICM) for solving partial differential equations. This method is different from the existing point interpolation method (PIM) that is based on the Galerkin weak-form. Because it is based on the collocation scheme no background cells are required for numerical integration. Radial basis functions are used in the work to create shape functions. A series of test examples were numerically analysed using the present method, including 1-D and 2-D partial differential equations, in order to test the accuracy and efficiency of the proposed schemes. Several aspects have been numerically investigated, including the choice of shape parameter c with can greatly affect the accuracy of the approximation; the enforcement of additional polynomial terms; and the application of the Hermite-type interpolation which makes use of the normal gradient on Neumann boundary for the solution of PDEs with Neumann boundary conditions. Particular emphasis was on an efficient scheme, namely Hermite-type interpolation for dealing with Neumann boundary conditions. The numerical results demonstrate that good improvement on accuracy can be obtained after using Hermite-type interpolation. The h-convergence rates are also studied for RPICM with different forms of basis functions and different additional terms. © 2005 Elsevier Ltd. All rights reserved.
Source Title: Computers and Mathematics with Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/61192
ISSN: 08981221
DOI: 10.1016/j.camwa.2005.02.019
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

32
checked on Dec 13, 2017

WEB OF SCIENCETM
Citations

25
checked on Dec 13, 2017

Page view(s)

39
checked on Dec 9, 2017

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.