Remark 3.1 We see from (3.19) and (3.20) that the errors |U(T) − uN(T)| and U −
uNT,N decay rapidly as N and r increase. The convergence rate is O(N−r). Thus, the
smoother the exact solution, the smaller the numerical errors. In other words, the
scheme (2.12) possesses the spectral accuracy.