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

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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.

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  1. Department of Mathematics, State University of New York at Buffalo, Buffalo, NY, 14260-2900, USA

    Xinjuan Chen & Jae-Hun Jung

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  1. Xinjuan Chen
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  2. Jae-Hun Jung
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Correspondence to Jae-Hun Jung.

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Chen, X., Jung, JH. Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers. J Sci Comput 51, 683–702 (2012). https://doi.org/10.1007/s10915-011-9526-y

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  • DOI: https://doi.org/10.1007/s10915-011-9526-y

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