I have a PDE in the form of $$ \frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} + u = \delta(x-1), $$ with initial condition $u(x,0)=100$. I'm trying to solve it numerically, but I have no idea on which method should I use. Most of the examples that I refer to has no delta function in the PDE.
Can anyone guide me on what should I do?
Thank you very much.