This is the <Backward Euler diffusion scheme> with a centered second spatial difference. Taylor expansion gives first order in time and second order in space:
$$
\tau=O(\Delta t)+O(\Delta x^2).
$$
With the parabolic scaling $\Delta t=\mu\Delta x^2$ and fixed $\mu$, the combined error is $O(\Delta x^2)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 341 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-341/3/a/solution