@Article{cmes.2011.071.157,
AUTHOR = {Ying-Hsiu  Shen, Chein-Shan  Liu},
TITLE = {A New Insight into the Differential Quadrature Method in Solving 2-D Elliptic PDEs},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {71},
YEAR = {2011},
NUMBER = {2},
PAGES = {157--178},
URL = {http://www.techscience.com/CMES/v71n2/25633},
ISSN = {1526-1506},
ABSTRACT = {When the local differential quadrature (LDQ) has been successfully applied to solve two-dimensional problems, the global method of DQ still has a problem by requiring to solve the inversions of ill-posed matrices. Previously, when one uses (n-1)th order polynomial test functions to determine the weighting coefficients with n grid points, the resultant n ×n Vandermonde matrix is highly ill-conditioned and its inversion is hard to solve. Now we use (m-1)th order polynomial test functions by n grid points that the size of Vandermonde matrix is m×n, of which m is much less than n. We find that the (m-1)th order polynomial test functions are accurate enough to express the solutions, and the novel method significantly improves the ill-condition of algebraic equations. Such a new DQ as being combined with FTIM (Fictitious Time Integration Method) can solve 2-D elliptic type PDEs successfully. There are some examples tested in this paper and the numerical errors are found to be very small.},
DOI = {10.3970/cmes.2011.071.157}
}