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

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:With the parabolic scaling $\Delta t=\mu \Delta x^2$ and fixed $\mu$, the combined error is $O(\Delta x^2)$.