Spectral methods are also very efficient at dealing with problems that are related to coordinate singularities. Indeed, if the basis functions fulfill the regularity requirements, then all the functions will automatically satisfy them. In particular, it makes the use of spherical coordinates much easier than with other methods, as explained in Section 3.2.
Another nice feature is the fact that a function can be represented either by its coefficients or its values at the collocation points. Depending on the operation one has to perform, it is easier to work with the one representation or the other. When working in the coefficient space, one takes full advantage of the nonlocality of the spectral representation. A lot of operations that would be difficult otherwise can then be easily performed, like computing the ratio of two quantities vanishing at the same point (see, for instance, ).
Living Rev. Relativity 12, (2009), 1
This work is licensed under a Creative Commons License.