Some Properties of DQ Weighting Coefficient Matrices
Chapter
Abstract
It has been shown in Chapters 2 and 3 that the DQ approximation for a derivative of any order has a similar form. The difference in the approximation for the respective derivatives lies only in the weighting coefficients. Consider a one-dimensional problem. It is supposed that there are N grid points in the whole domain with coordinates x1, x2, …, xN. At any location xi, the nth order derivative of a function u(x,t) with respect to x can be approximated by the DQ method as
for i = 1.2 ...,N
$$
u_x^{\left( n \right)}\left( {{x_i},t} \right) = \sum\limits_{j = 1}^N {w_{ij}^{\left( n \right)}} u\left( {{x_j},t} \right),
$$
(4.1)
Keywords
Weighting Coefficient Differential Quadrature Eigenvalue Distribution Grid Versus Convection Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag London 2000