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.
N. A. Libre et al., "Stable PDE Solution Methods for Large Multiquadric Shape Parameters," CMES - Computer Modeling in Engineering and Sciences, vol. 25, no. 1, pp. 23-41, Tech Science Press, Jan 2008.
Civil, Architectural and Environmental Engineering
Keywords and Phrases
Asymmetric collocation; Improved truncated singular value decomposition; Meshless radial basis functions; Multiquadric; Partial differential equations
International Standard Serial Number (ISSN)
Article - Journal
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