Integrated errors

Focus: norm of the numerical error $$||e^n||_{\ell^2} = \sqrt{\Delta t\sum_{n=0}^{N_t} ({\uex}(t_n) - u^n)^2}$$

Forward and Backward Euler: $$||e^n||_{\ell^2} = \frac{1}{4}\sqrt{\frac{T^3}{3}} a^2\Delta t$$

Crank-Nicolson: $$||e^n||_{\ell^2} = \frac{1}{12}\sqrt{\frac{T^3}{3}}a^3\Delta t^2$$