Date: Feb 16, 2013 11:51 PM
Author: AMX
Subject: Re: Crank Nikolson scheme for semi linear parabolic equations
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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