DOI: 10.1002/num.10062. Exponential convergence and <i>H‐c</i> multiquadric collocation method for partial differential equations

Exponential convergence and H‐c multiquadric collocation method for partial differential equations

10.1002/num.10062

Crossref journal-article

Wiley

Numerical Methods for Partial Differential Equations (311)

Abstract

AbstractThe radial basis function (RBF) collocation method uses global shape functions to interpolate and collocate the approximate solution of PDEs. It is a truly meshless method as compared to some of the so‐called meshless or element‐free finite element methods. For the multiquadric and Gaussian RBFs, there are two ways to make the solution converge—either by refining the mesh size h, or by increasing the shape parameter c. While the h‐scheme requires the increase of computational cost, the c‐scheme is performed without extra effort. In this paper we establish by numerical experiment the exponential error estimate ϵ ∼ O(λ√c̄h) where 0 < λ < 1. We also propose the use of residual error as an error indicator to optimize the selection of c. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 571–594, 2003

Bibliography

Cheng, A. H. âD., Golberg, M. A., Kansa, E. J., & Zammito, G. (2003). Exponential convergence and Hâc multiquadric collocation method for partial differential equations. Numerical Methods for Partial Differential Equations, 19(5), 571â594. Portico.

Authors 4

A. H.‐D. Cheng (first)
M. A. Golberg (additional)
E. J. Kansa (additional)
G. Zammito (additional)

References 67 Referenced 299

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Dates

Type	When
Created	22 years, 2 months ago (May 23, 2003, 6:02 a.m.)
Deposited	1 year, 9 months ago (Nov. 17, 2023, 9:11 p.m.)
Indexed	21 hours, 58 minutes ago (Aug. 20, 2025, 8:57 a.m.)
Issued	22 years, 3 months ago (April 22, 2003)
Published	22 years, 3 months ago (April 22, 2003)
Published Online	22 years, 3 months ago (April 22, 2003)
Published Print	21 years, 11 months ago (Sept. 1, 2003)

Funders 0

None

BibTeX

@article{Cheng_2003, title={Exponential convergence and H‐c multiquadric collocation method for partial differential equations}, volume={19}, ISSN={1098-2426}, url={http://dx.doi.org/10.1002/num.10062}, DOI={10.1002/num.10062}, number={5}, journal={Numerical Methods for Partial Differential Equations}, publisher={Wiley}, author={Cheng, A. H.‐D. and Golberg, M. A. and Kansa, E. J. and Zammito, G.}, year={2003}, month=apr, pages={571–594} }

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