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

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 AMX Posts: 35 Registered: 8/22/09
Re: discretizing laplacian
Posted: Mar 1, 2013 6:02 AM

On Mon, 25 Feb 2013 07:09:32 -0800 (PST),
Sandeep Kumar <searchsandy1712@gmail.com> wrote:

> 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).
>

Change the order. Spatial discretisation first, so you'll get
some equation

?u(t)/?t = F(u,x,t)
where nonlinear F depends on set of points x_i and values of u(x_i).

Then for t=t_k
?u(t_k)/?t = F(u,x,k_i)
and for t=t_{k+1}
?u(t_{k+1})/?t = F(u,x,t_{k+1})

Their average gives you the CN expression. After reordering
you'll get nonlinear equations dependent on both known u(x_i,t_k)
and sought u(x_i,t_{k+1})

AMX

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