Neumann Boundary Conditions using FTCS on the Heat Equation

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tlonster
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I am really confused with the concept of Neumann Boundary conditions. For the simple PDE

ut=uxx for the domain from 0<=x<=1

I'm trying to use a ghost point (maintain a second order scheme) for the Neumann Boundary condition ux(0,t) = 0.

I understand that I can setup a scheme to calculate u(0,t) by

u(0,n+1) = (1-2r)u(0,n) + 2ru(1,n)

What are the u(0,n) and u(1,n) representative of?

I'm given u(x,0) = sin((3*∏)/2)(x+(1/3))

Any help would be appreciated to help me understand what those inputs actually are.
Thanks
 

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