Hi. Been a while since I logged in here, I missed this place. Anyway, I have a question (title). Is that even possible? Say for example I have the standard heat equation (PDE) subject to the boundary conditions: T(0,t) = To T(∞,t) = Ti And the initial condition: T(0,t) = Ti I am aware of how to solve this analytically. I would like to try solving it numerically - using finite difference methods. However, I have no idea how will I discretize something that is infinite... What I did is assume x to be a gigantic value (which would become very unwieldy if my spatial step is something like 0.0001). Then, at the final spatial point, either I assume that the derivative is zero (because apparently if I compare it with the analytical solution by having t = a very large value, then run the numerical simulation for a very long time, both dependent values will become To) or just set the value to be equal to Ti (but I run at the difficulty of having the last point still equal to Ti at large time values). So my question is: How is it possible to discretize infinite boundaries effectively? Thanks! PS: I know that this is graduate-level math, but please talk to me in layman's language. I easily get inebriated if you guys bring out complex terms suddenly. Thanks.