Open Access

ARTICLE

Stable PDE Solution Methods for Large Multiquadric Shape Parameters

Arezoo Emdadi¹, Edward J. Kansa², Nicolas Ali Libre^1,3, Mohammad Rahimian¹, Mohammad Shekarchi¹
1 Department of Civil Engineering, University of Tehran, Tehran, Iran
2 E.J. Kansa*, Department of Mechanical and Aeronautical Engineering, University of California, Davis, Davis, CA95616-5294 USA. email: ejkansa@ucdavis.edu
3 Corresponding author, Nicolas Ali Libre, email : nalibre@ut.ac.ir

Computer Modeling in Engineering & Sciences 2008, 25(1), 23-42. https://doi.org/10.3970/cmes.2008.025.023

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.

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Keywords

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