Note the shunting yard algorithm is an iterative (as opposed to recursive) version of Pratt parsing (and also precedence climbing which is virtually identical). However as normally stated it does not do proper error checking - it will accept totally invalid input.

That isn't a fundamental limit of the algorithm though; you can easily add error checking, as I did here: https://github.com/Timmmm/expr/blob/1b0aef8f91460974d526b5ba...

I'm not really sure why this is omitted.