Post by matthorr on Nov 9, 2015 16:06:53 GMT
I'm posting the solution (probably wrong) that I came up with. Did anyone else get something different? I'm not quite sure what to make of the dispersion term.
\[ u_t+au_x=\frac{\Delta x}{2}\left[\frac{\Delta x}{\Delta t}-a\left(\frac{a\Delta t}{\Delta x}\right)\right]u_xx+\frac{a\Delta x}{2}\left[\frac{a\Delta t}{3}\left(\frac{a\Delta t}{\Delta x}\right)-\frac{\Delta x}{2\Delta t}-\frac{\Delta x}{3}\right] \]
\[ u_t+au_x=\frac{\Delta x}{2}\left[\frac{\Delta x}{\Delta t}-a\left(\frac{a\Delta t}{\Delta x}\right)\right]u_xx+\frac{a\Delta x}{2}\left[\frac{a\Delta t}{3}\left(\frac{a\Delta t}{\Delta x}\right)-\frac{\Delta x}{2\Delta t}-\frac{\Delta x}{3}\right] \]