TY  - EJOU
AU  - Shen, Ying-Hsiu  
AU  - Liu, Chein-Shan  

TI  - A New Insight into the Differential Quadrature Method in Solving 2-D Elliptic PDEs
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2011
VL  - 71
IS  - 2
SN  - 1526-1506

AB  - 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.
KW  - Differential quadrature (DQ)
KW  -  Vandermonde matrix
KW  -  Fictitious time integration method (FTIM)
KW  -  Dirichlet boundary conditions
KW  -  Elliptic Partial differential equations

DO  - 10.3970/cmes.2011.071.157