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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: $$ ||e^n||_{\ell^2} = \frac{1}{12}\sqrt{\frac{T^3}{3}}a^3\Delta t^2$$
Analysis of both the pointwise and the time-integrated true errors:
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