```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 vectorwhile ?(?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 ofalgebraic equations. In the case of nonlinear PDEs it leads tononlinear algebaric equations. You have to solve nonlinear set ofequations at each step.I've never worked with CH equation but first what I think of isthat u is in range (-1, 1), then the term u^3 is small incomparision to u. Defining new field p=u^3 would lead to iterativeprocess of searching n-th approximation of u field withF(u_(n),p_(n-1))=0 with p_0=0.  It just the first idea; I do notknow if this works.   AMX-- adres w rot13Nyrxfnaqre Znghfmnx r-znk@b2.cy
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