If somebody doesn’t know what a PDE is, then it is very likely that
PartialDifferentialEquation would not enlighten the person any further, so
why would the longer name be more useful?
If you have ever studied differential equations though, then you would
immdediately know what a PDE is.
Same with ODE and SVD.
It’s an interesting debate, which I dont claim to know the answer to, but I
think if spelling out the acronym doesn’t help people understand the
meaning, then there is no point in spelling it out.
The full spelling should be definitely used in cases of ambiguity or when
the spelled out name is more eplanatory to the unititiated.
But in the case of PDE, if somebody doesnt know what PDE is, then
PartialDifferentialEquation is not going to explain it any better, and if
you know what a partial DE is, then the PDE acronym will be entirely clear.