How do I find a DE that is consistent with:

$\displaystyle u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)$

Also, when is the scheme stable?

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- Jun 10th 2012, 11:58 AMBorkborkmathFind the DE that is consistent with this method
How do I find a DE that is consistent with:

$\displaystyle u_j^{n+1}=\frac{1}{2}(u_{j+1}^n+u_{j-1}^n)-\frac{1}{2}\frac{\Delta t}{(\Delta x)^3}(u_{j+2}^n-2u_{j-1}^n-u_{j-2}^n)$

Also, when is the scheme stable? - Jun 10th 2012, 12:34 PMBobPRe: Find the DE that is consistent with this method
Are you sure about that $\displaystyle (\Delta x)^{3}$ ?

- Jun 10th 2012, 01:03 PMBorkborkmathRe: Find the DE that is consistent with this method
Yes I am :\

- Jun 11th 2012, 12:52 AMBobPRe: Find the DE that is consistent with this method
Too bad, $\displaystyle (\Delta x)^{2}$ and I could probably offer some help. I'm not familiar with methods involving $\displaystyle (\Delta x)^{3}$.

- Jun 11th 2012, 11:18 AMBorkborkmathRe: Find the DE that is consistent with this method
can you offer your help for the x^2? And I'll see what I can do to change it for x^3?

- Jun 12th 2012, 12:00 AMBobPRe: Find the DE that is consistent with this method
It's just textbook stuff. Look at the section on the solutions of parabolic equations.