|
|
|
We apply the Backward Euler scheme to each component equation: $$ [D_t^- u = v]^{n+1},$$ $$ [D_t^- v = -\omega u]^{n+1} \tp $$ Written out: $$ \begin{align} u^{n+1} - \Delta t v^{n+1} = u^{n},\\ v^{n+1} + \Delta t \omega^2 u^{n+1} = v^{n} \tp \end{align} $$ This is a coupled \( 2\times 2 \) system for the new values at \( t=t_{n+1} \)!
|
|
|