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Correction terms in the Crank-Nicolson scheme (1)

[Dtu=a¯ut]n+12, Definition of the truncation error R and correction terms C: [Dtue+a¯uet=C+R]n+12.

Must Taylor expand

Cn+12+Rn+12=124ue Let C^{n+\half} cancel the \Delta t^2 terms: C^{n+\half} = \frac{1}{24}\uex'''(t_{n+\half})\Delta t^2 + \frac{a}{8}\uex''(t_{n})\Delta t^2\tp

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