Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 51, Issue 3, Pages 683-702Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-011-9526-y
Keywords
Multiquadric radial basis functions; Numerical stability; Matrix stability; Eigenvalue stability; CFL condition
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Funding
- Div Of Biological Infrastructure
- Direct For Biological Sciences [0959870] Funding Source: National Science Foundation
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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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