Guys… GUYS! You are all flagging me, sending me passive/aggressive emails but all of you are out topic as hell. Rafael Bailo (and myself) are specialist of numerical PDEs, and we are both extremely, acutely aware of all your off topic ramblings… But the thing is: for this practical application we have in mind, which is related to thermonuclear fusion theory, we awfully need to know the full discrete spectrum.
Yes.
The. Full. Spectrum. Of. The. Discrete. Problem.
If we knew how to compute the continuous spectrum (which consists of an uncountable, essential part, a countable, discrete part AND some eigenvalues), we wouldn’t need to check the discretized one.
But we don’t.