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AMX
Posts:
35
Registered:
8/22/09


Re: Nonhomogeneous 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 nonhomogeneous 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 nonhomogeneous b.c. and v is sought and has to satisfy homogeneous b.c.
?^2(u0+v)?(u0+v)=0
AMX
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