Abstract: We studied the numerical approximation to Cahn-Hilliard equation with pseudo-spectral method. We proved the convergence and the st ability of the semi-discrete and the full-discrete soltions to the real solution and figured out the corresponding rate of the convergence. Finaly, we obtained the blow-up phenomena of the semi-discrete problem’s solution.

Key words: pseudo-spectral method, interpolation operator, blow-up