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Title: Multilevel sparse grids collocation for linear partial differential equations, with tensor product smooth basis functions
Authors: Zhao, Yangzhang
Zhang, Qi
Levesley, Jeremy
First Published: 27-Nov-2017
Publisher: Elsevier
Citation: Computers and Mathematics with Applications, 2017
Abstract: Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis} shows good convergence. In this paper we use a sparse kernel basis for the solution of PDEs by collocation. We will use the form of approximation proposed and developed by Kansa \cite{Kansa1986}. We will give numerical examples using a tensor product basis with the multiquadric (MQ) and Gaussian basis functions. This paper is novel in that we consider space-time PDEs in four dimensions using an easy-to-implement algorithm, with smooth approximations. The accuracy observed numerically is as good, with respect to the number of data points used, as other methods in the literature; see \cite{Langer1,Wang1}.
DOI Link: 10.1016/j.camwa.2017.10.014
ISSN: 0898-1221
Embargo on file until: 27-Nov-2018
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, Elsevier. Deposited with reference to the publisher’s open access archiving policy.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.
Appears in Collections:Published Articles, Dept. of Mathematics

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