In a paper that appeared in volume 2 (2011) of SIAM Financial Mathematics by R. Cont, N. Lantos and the author, it was shown that by writing the solution of the Black-Scholes partial dierential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we show that it is in fact a P.O.D. method and in some other variable it is also a spectral method. It allows us to nd a good preconditioning matrix to minimize the ill conditioned linear system, and even have explicit solutions.