# Find the DE that is consistent with this method

• Jun 10th 2012, 11:58 AM
Borkborkmath
Find 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 PM
BobP
Re: Find the DE that is consistent with this method
Are you sure about that $\displaystyle (\Delta x)^{3}$ ?
• Jun 10th 2012, 01:03 PM
Borkborkmath
Re: Find the DE that is consistent with this method
Yes I am :\
• Jun 11th 2012, 12:52 AM
BobP
Re: 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 AM
Borkborkmath
Re: 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 AM
BobP
Re: Find the DE that is consistent with this method
It's just textbook stuff. Look at the section on the solutions of parabolic equations.