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A collocation method using new combined radial basis functions of thin plate and multiquadraic types
Faculty
Science
Year:
2006
Type of Publication:
Article
Pages:
697-701
Authors:
Ahmed, S. G
DOI:
10.1016/j.enganabound.2006.03.001
Journal:
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS ELSEVIER SCI LTD
Volume:
30
Research Area:
Engineering; Mathematics
ISSN
ISI:000239875300007
Keywords :
meshless methods, thin plate radial basis method, multiquarraic radial basis method, implicit finite difference approximations
Abstract:
The meshless methods for solving boundary value problems have been extensively popularised owing to their flexibility in engineering applications. In the present paper, a meshless method based on a new combination between thin plate and multiquadraic radial basis functions is developed. The new form of the radial basis function contains a parameter epsilon, which named a control parameter, 0 <= epsilon <= 1. Starting the proposed method by the classical Theta-weight implicit finite difference approximation, then fellow up the same procedure as thin plate or multiquadraic but with the new form of the radial basis function. The parameter, epsilon will take zero when evaluating the diagonal elements for the coefficients matrix resulted. Two different examples were solved with different dimensionality and the present results were compared with the analytical results and gave a good agreement. (C) 2006 Elsevier Ltd. All rights reserved.
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