Hi. Been a while since I logged in here, I missed this place.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# A PDE discretization for semi-infinite boundary?

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