||CMES: Computer Modeling in Engineering & Sciences, Vol. 25, No. 1, pp. 23-42, 2008
||Full length paper in PDF format. Size = 1,313,024 bytes
||meshless radial basis functions, multiquadric, asymmetric collocation, partial differential equations,improved truncated singular value decomposition
||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.