@Article{cmes.2008.025.023, AUTHOR = {Arezoo Emdadi, Edward J. Kansa, Nicolas Ali Libre,3, Mohammad Rahimian, Mohammad Shekarchi}, TITLE = {Stable PDE Solution Methods for Large Multiquadric Shape Parameters}, JOURNAL = {Computer Modeling in Engineering \& Sciences}, VOLUME = {25}, YEAR = {2008}, NUMBER = {1}, PAGES = {23--42}, URL = {http://www.techscience.com/CMES/v25n1/25090}, ISSN = {1526-1506}, 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.}, DOI = {10.3970/cmes.2008.025.023} }