Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers

The fully discretized multiquadric radial basis function methods for hyperbolic equations are considered. We use the matrix stability analysis for various methods, including the single and multi-domain method and the local radial basis function method, to find the stability condition. The CFL condit...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 51; no. 3; pp. 683 - 702
Main Authors: Chen, Xinjuan, Jung, Jae-Hun
Format: Journal Article
Language:English
Published: Boston Springer US 01.06.2012
Springer Nature B.V
Subjects:
Algorithms
Boundary conditions
Computational Mathematics and Numerical Analysis
Hyperbolic functions
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Radial basis function
Stability analysis
Theoretical
Matrix stability
Multiquadric radial basis functions
Numerical stability
CFL condition
Eigenvalue stability
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:The fully discretized multiquadric radial basis function methods for hyperbolic equations are considered. We use the matrix stability analysis for various methods, including the single and multi-domain method and the local radial basis function method, to find the stability condition. The CFL condition for each method is obtained numerically. It is explained that the obtained CFL condition is only a necessary condition. That is, the numerical solution may grow for a finite time. It is also explained that the boundary condition is crucial for stability; however, it may degrade accuracy if it is imposed.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-011-9526-y