Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: discretizing laplacian
Replies: 2   Last Post: Mar 1, 2013 6:02 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Spellucci

Posts: 214
Registered: 11/9/09
Re: discretizing laplacian
Posted: Feb 26, 2013 8:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Sandeep Kumar <searchsandy1712@gmail.com> writes:
>Can anybody please tell me how to discretize Laplacian. I have -
>laplacian(Un^2.Un+1), which is laplacian of product of Un^2 and Un+1.
>where Un is U(j,n) and Un+1 is U(j,n+1).
>
> Thanks in advance.
>Regards

this makes no sense for me: with U already discretized, what should
laplacian of this mean?
If I remember right you one had laplacian(u^3) plus Crank-Nicholson,
that means you need
1/2*(laplacian(u(x,t_n)^3)+laplacian(u(x,t_{n+1})^3))
where of course laplacian is w.r.t x and -fortunately- x is onedimensional.
method 1:
(d/dx)^2(u(x,t_n)^3)(x=x_i) = 3u(i,n)^2(u(i+1,n)-2u(i,n)+u(i-1,n))/h^2
+(6/h^2)(u(i+1,n)-u(i-1,n))^2
method2:
(d/dx)^2(u(x,t_n)^3) =
(1/h)^2 ( ((u(i+1,n)^2+u(i,n)^2)/2)*(u(i+1,n)-u(i,n))
- ((u(i,n)^2+u(i-1,n)^2)/2)*(u(i,n)-u(i-1,n)) )

hth
peter




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.