You have a PDE:

and you discretize the advection term and the diffusion term.
Question: in your discretized model…

where does the first RHS term u[i] come from in the original PDE?
You have a PDE:

and you discretize the advection term and the diffusion term.
Question: in your discretized model…

where does the first RHS term u[i] come from in the original PDE?