Stable PDE Solution Methods for Large Multiquadric Shape Parameters
Arezoo Emdadi; Edward J. Kansa; Nicolas Ali Libre; Mohammad Rahimian; and Mohammad Shekarchi

doi:10.3970/cmes.2008.025.023
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 25, No. 1, pp. 23-42, 2008
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Keywords meshless radial basis functions, multiquadric, asymmetric collocation, partial differential equations,improved truncated singular value decomposition
Abstract We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination.
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