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

Authors:
Xinjuan Chen;Jae-Hun Jung
Affiliations:
Department of Mathematics, State University of New York at Buffalo, Buffalo, USA 14260-2900;Department of Mathematics, State University of New York at Buffalo, Buffalo, USA 14260-2900
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

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.