MATLAB: FFT with specified modes

Question

Using MATLAB I want to implement some kind of a spectral method. The idea is as following (described for a example which is working).

1. Dirichlet (and Neumann, and periodic) boundaries leads to eigenvalues in the fourier space of k=n*pi/L

2. Projecting all the linear operators in the fourier space to the discretized k-values:

   e.g. L = -D*(k.*k) (for diffusion only)

3. Defining the propagator in time as P = exp( dt * L )

4. Calculating iteratively the evolution in time by uh_{n+1} = uh_n * P

5. return the calculated value to the real space every time I want to save the value by ifft( uh )

My question concerns another boundary conditions.

In my case I have Robin boundary conditions. So, the eigenvalues are defined through some weird equation of the form tan( x ) = x or the like. The problem of computing them is solved.

As I have the values, the step no. 2 and 3 is simple too, but:

For applying P on the fourier-transformed vector uh I have to ensure that my uh = fft(u) uses the same eigenvalues, which is not the case by default.

By default MATLAB uses equidistant modes for the fft.

Is there any simple trick for this?

Or, maybe, do I have any mistake in my thoughts?