TY  - EJOU
AU  - Emdadi, Arezoo  
AU  - Kansa, Edward J.  
AU  - Libre, Nicolas Ali  
AU  - Rahimian, Mohammad 
AU  - Shekarchi, Mohammad  

TI  - Stable PDE Solution Methods for Large Multiquadric Shape Parameters
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2008
VL  - 25
IS  - 1
SN  - 1526-1506

AB  - 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.
KW  - meshless radial basis functions
KW  -  multiquadric
KW  -  asymmetric collocation
KW  -  partial differential equations
KW  -  improved truncated singular value decomposition

DO  - 10.3970/cmes.2008.025.023