# Explicit vs. implicit FDM: reference needed

The following is my latest post at iMechanica [^]:

“The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).

Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).

It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.

However, with some simple Google searches (and browsing through some 10+ books I could lay my hands on), I could not find any prior paper/text to cite by way of a reference.

I feel sure that it must have appeared in some or the paper (or perhaps even in a text-book); it’s just that I can’t locate it.

So, here is a request: please suggest me a reference where this observation (about the local vs. global support of the solution) is noted explicitly. Thanks in advance.

Best,

–Ajit

[E&OE]”

Self-explanatory, right?

[E&OE]