Hans Johnston May 14 2004 I wrote a program to compute D2, extract the interior, and then find the evals and evectors. The results match, at least to roundoff, MATLAB results. Note that MATLAB produces the eigenvalues in EXACTLY the same order since they use LAPACK. I compute D1 and D2 using a different algorithm then that given in Trefethen's cheb.m. I'll explain the reason for the change later. Note also that I index from 0:m, thus D2int(1:m-1,1:m-1), and that my CHEBD program only asks for m. I suggest starting indices from 0 for problems with boundaries. I will work on (hopefully) in the next few days a Poisson solver. I have never used FFTW, although will do so in the future. In the meantime I will use the vfftpk.f routines since I am very familiar with them. Using the REAL transform is very straightforward.