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Multilevel sparse grids collocation for linear partial differential equations, with tensor product smooth basis functions

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posted on 2017-11-21, 09:55 authored by Yangzhang Zhao, Qi Zhang, Jeremy Levesley
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}.

History

Citation

Computers and Mathematics with Applications, 2017

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Computers and Mathematics with Applications

Publisher

Elsevier

issn

0898-1221

Acceptance date

2017-10-19

Copyright date

2017

Available date

2018-11-27

Publisher version

https://www.sciencedirect.com/science/article/pii/S0898122117306624

Notes

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.

Language

en

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