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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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
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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.
AbstractList	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.
Author	Jung, Jae-Hun Chen, Xinjuan
Author_xml	– sequence: 1 givenname: Xinjuan surname: Chen fullname: Chen, Xinjuan organization: Department of Mathematics, State University of New York at Buffalo – sequence: 2 givenname: Jae-Hun surname: Jung fullname: Jung, Jae-Hun email: jaehun@buffalo.edu organization: Department of Mathematics, State University of New York at Buffalo
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Cites_doi	10.1017/CBO9780511543241 10.1016/j.amc.2009.08.037 10.1016/j.apnum.2006.02.006 10.1016/S0168-9274(02)00107-1 10.1016/j.camwa.2007.01.028 10.1016/j.apnum.2004.07.004 10.1007/978-3-540-46222-4_3 10.1016/j.camwa.2006.06.005 10.1016/j.cpc.2010.08.035 10.1016/S0898-1221(01)00299-1 10.1098/rspa.2009.0033 10.1137/090774707 10.1016/0898-1221(90)90271-K 10.1137/040610143 10.1016/j.camwa.2006.04.007 10.1007/BF02432002 10.1029/2009GC002985 10.1109/TMAG.2008.2001796 10.1002/num.20290 10.2514/6.1997-1939
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Snippet	The fully discretized multiquadric radial basis function methods for hyperbolic equations are considered. We use the matrix stability analysis for various...
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SubjectTerms	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
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Title	Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers
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