Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 63 / 3 / 1 / Solution

Put $h=\Delta x$. The spatial operator is the sum of a centred $x$ difference and a dissipative second-order forward advection stencil in $y$. For a smooth function, their Taylor expansions giveThus the leading spatial local truncation error is $h^2(u_{xxx}/6-u_{yyy}/3)$, generally nonzero. The semidiscretization is second order in space. Time has not yet been discretized, so there is no separate time order or time-step condition at this stage.