Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Entire DC Network
Stable Pde Solution Methods For Large Multiquadric Shape Parameters, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
Stable Pde Solution Methods For Large Multiquadric Shape Parameters, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
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.