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Error estimates of local multiquadric‐based differential quadrature (LMQDQ) method through numerical experiments
Author(s) -
Ding H.,
Shu C.,
Tang D. B.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1318
Subject(s) - mathematics , taylor series , approximation error , quadrature (astronomy) , numerical integration , mathematical analysis , nyström method , gauss–jacobi quadrature , numerical approximation , numerical differentiation , numerical analysis , polynomial , gauss–kronrod quadrature formula , integral equation , physics , optics
In this article, we present an error estimate of the derivative approximation by the local multiquadric‐based differential quadrature (LMQDQ) method. Radial basis function is different from the polynomial approximation, in which Taylor series expansion is not applicable. So, the present analysis is performed through the numerical solution of Poisson equation. It is known that the approximation error of LMQDQ method depends on three factors, i.e. local density of knots h , free shape parameter c and number of supporting knots n s ). By numerical experiments, their contribution to the approximation error and correlation were studied and analysed in this paper. An error estimate ε ∼ O (( h / c ) n ) is thereafter proposed, in which n is a positive constant and determined by the number of supporting knots n s . Copyright © 2005 John Wiley & Sons, Ltd.