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The scheme $$ [D_t u = \dfc D_xD_x \overline{u}^x]^{n+\half}_q$$ leads to $$ A = \frac{ 1 - 2F\sin^2p}{1 + 2F\sin^2p} $$ $$ u^n_q = \left(\frac{ 1 - 2F\sin^2p}{1 + 2F\sin^2p}\right)^ne^{ikp\Delta x}$$
Stability: The criteria \( A>-1 \) and \( A < 1 \) are fulfilled for any \( \Delta t >0 \)
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