Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 69 / 2 / a / Solution

Evaluating a variable diffusion coefficient at both adjacent half-grid points makes odd spatial Taylor terms cancel. The conservative spatial bracket is $h^2(au_x)_x+O(h^4)$, yielding a fourth-order one-step residual when the forward time step is proportional to $h^2$.


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 Incoming links: Symmetric half-grid diffusion consistency