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Say I am solving a PDE as [itex]\frac{\partial y^2}{\partial^2 x}+\frac{\partial y}{\partial x}=f[/itex], with the boundary condition [itex]y(\pm L)=A[/itex]. I can understand for the second order differential term, there two boundary conditions are well suited. But what about the first order differential term? Imposing at the same time these two boundary condition will be redundant for that term, isn't it?

I came across this when I use spectral method to solve the PDE with Dirichlet BC ([itex]y(\pm 1)=0[/itex]) at the two ends. When constructing the matrix for the D^2 term, I get rid of the first and last row and columns. It's easy and it makes sense. But when I tried to construct the D term, what should I do then?

Thanks a lot.

Jo