NDSolve to solve a PDE with a periodic boundary condition, for example,
"DifferenceOrder"->"Pseudospectral" but without
PeriodicInterpolation->True. After I obtained the solution, I plotted the grid and found that the grid used was uniform.
But according to the Mathematica tutorial:
The pseudospectral derivative approximation is only applicable when the grid points are spaced corresponding to the Chebyshev–Gauss–Lobatto points or when the grid is uniform with
This means that if one uses
DifferenceOrder"->"Pseudospectral but doesn't add
PeriodicInterpolation->True the grid should have consisted of the Chebyshev–Gauss–Lobatto points, that is, it should be nonuniform. Nevertheless, based on the fact that the grid used in the abovementioned computation was uniform by only using a periodic boundary condition but never applying
PeriodicInterpolation->True, could we say that a periodic boundary condition implies
Thank you for any suggestion.