Is there any particular criterion with which we decide upon which grid point to select for analysis? I have used equations given in the review paper by C.W.Bert and M.Malik. I am working on the free vibration of Euler beam. What should be kept in mind while selecting the grid points?
You need to choose points at the boundary condition, so you can satisfy them. You also need to add enough interior points to obtain a good approximation of the shape of the interior response.
If you do not need boundary points, orthogonal Gauss points are the best choice. It is because of theirs maximal order of convergence and small Lebesque constant (in Chebyshev Gauss case this constant is minimal). But if you need boundary points, Gauss Lobatto points are very good choices. It is because of theirs high order of accuracy. To more details see spectral methods books in the literature.
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