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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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