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Topic: Crank Nikolson scheme for semi linear parabolic equations
Replies: 1   Last Post: Feb 16, 2013 11:51 PM

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 AMX Posts: 35 Registered: 8/22/09
Re: Crank Nikolson scheme for semi linear parabolic equations
Posted: Feb 16, 2013 11:51 PM
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On Sat, 16 Feb 2013 07:27:19 -0800 (PST), Sandeep Kumar
<searchsandy1712@gmail.com> wrote:

> Can anybody help me with this?
> I am trying to implement a fourth order semi linear parabolic
> equation called as Cahn-Hilliard equation, in MatLab.
> Its given by
> del u/ del t = - epsilonsquare* laplacian^2(u)+ laplacian(u^3)-lapacian(u)

It cannot be in that form. For scalar field u, ?u is a vector
while ?(?u) is a scalar. You cannot add a scalar to a vector.

I've checked it at wiki and there is a bit different form.

> Can anybody please tell me how to deal with these non-linear terms?

In the case of linear PDEs discrete form leads to linear set of
algebraic equations. In the case of nonlinear PDEs it leads to
nonlinear algebaric equations. You have to solve nonlinear set of
equations at each step.

I've never worked with CH equation but first what I think of is
that u is in range (-1, 1), then the term u^3 is small in
comparision to u. Defining new field p=u^3 would lead to iterative
process of searching n-th approximation of u field with
F(u_(n),p_(n-1))=0 with p_0=0. It just the first idea; I do not
know if this works.

AMX

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