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Topic: Non-homogeneous Dirichlet boundary condition in an eigenvalue
problem

Replies: 1   Last Post: Apr 9, 2013 6:24 AM

 AMX Posts: 35 Registered: 8/22/09
Re: Non-homogeneous Dirichlet boundary condition in an eigenvalue
problem

Posted: Apr 9, 2013 6:24 AM

On Fri, 5 Apr 2013 15:30:30 -0700 (PDT), Mengqi Zhang
<jollage@gmail.com> wrote:
> Hi All,
>
> I know that in using spectral method to solve the eigenvalue
> problem, if the boundary condition for eigenfunction is
> homogeneous Dirichlet type (i.e., u(+1)=u(-1)=0), we will just
> delete the first and last rows and columns.
>
> But what if the boundary condition is non-homogeneous Dirichlet
> type? Say to solve the eigenfunction of D^2 with the boundary
> condition u(+1)=1 and u(-1)=0.
>
> Remember that we are in a eigenvalue problem, which is here D^2
> u = lambda u.
>

Decompose your problem into pair of functions:
u=u0+v,
where u0 is arbitrary and has to satisfy non-homogeneous b.c.
and v is sought and has to satisfy homogeneous b.c.

?^2(u0+v)-?(u0+v)=0

AMX

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