Convergence of non-stationary semi-discrete RBF schemes for the heat and wave equation

We give a detailed analysis of the convergence in Sobolev norm of the method of lines for the classical heat and wave equations on R n using non-stationary radial basis function interpolation on regular grids h Z n (scaled cardinal interpolation), for basis functions whose native space is a Sobolev...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 49; no. 5
Main Author Brummelhuis, Raymond
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2023
Springer Nature B.V
Subjects
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Convergence
Interpolation
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Method of lines
Radial basis function
Sobolev space
Visualization
Wave equations
65M15
Radial basis function interpolation
41A25
65D12
65M70
Rate of convergence
41A05
65M12
Semi-discrete collocation schemes (method of lines)
65M20
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ISSN1019-7168
1572-9044
DOI10.1007/s10444-023-10058-8

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Summary:We give a detailed analysis of the convergence in Sobolev norm of the method of lines for the classical heat and wave equations on R n using non-stationary radial basis function interpolation on regular grids h Z n (scaled cardinal interpolation), for basis functions whose native space is a Sobolev space of order ν / 2 with ν > n + 2 .
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-023-10058-8