When using NDSolve
to solve a PDE with a periodic boundary condition, for example,
$y(0,t)=y(L,t)$ using "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 PeriodicInterpolation->True
,
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 PeriodicInterpolation->True
.
Thank you for any suggestion.