Stable PDE solution methods for large multiquadric shape parameters

作者：Emdadi Arezoo; Kansa Edward J; Libre Nicolas Ali^*; Rahimian Mohammad; Shekarchi Mohammad

来源：Computer Modeling in Engineering & Sciences, 2008, 25(1): 23-41.

• 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 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.

• 出版日期2008-2