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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


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 CahnHilliard 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 nonlinear 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 nth approximation of u field with F(u_(n),p_(n1))=0 with p_0=0. It just the first idea; I do not know if this works.
AMX
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