Umm.. no, you don't. Currently it looks like ships are just ordered to follow their enemies. This is much simpler than attempting to forecast where an enemy ship is heading.

Yeah, but you still have several ships simultaneously calculating their routes

There aren't many calculations in a straight line

No, and there aren't that many calculations involved in acceleration, either. Maybe 2-3 times as complex as a straight line, once you know acceleration of the "target" point.

not only is the computer keeping track of where all the ships are you can see. it is also keeping track of all the ships you can't see.

a real spaceship would only keep track of the ship it is tracking not the ones 5 star systems away.

and nasa keeps track of every bit of trash and rocks in orbit down to i think 5"

Really only one simple trig equation, in witch all you are looking for is lead angle . . this has to be one only so often at this rather slow speed of ship movement - no need for constant updates, does not have to be exact and needs to be only done once per Group of ships not single ships if they all stick together (fighters may need there own . . or not because they move so fast) . . we are looking to get them into a combat envelop and once in no need to lead anymore.
A real no brainier to setup and lots of ways to optimize and streamline.

Which will give virtually the same result as the turn notifications I mentioned earlier. I couldn't tell you which is better without looking at Ironclad's engine.

Of course, neither method plots a true long-range intercept course, but they should allow the pursuing ship to cut enough corners to make up some time.

Well, not exactly . .
All you need is the other ships vector which is already generated by the engine. The greater the deflection and speed (this could be simple, 2 numbers, top speed of fast or show ship no since in getting the real numbers since these ships always travel at top speed and accelerate to top speed quickly and we really have only 2 classes - though fighers are different case). Now if you want more . . factor in your distance and speed . . again precision is not needed.
Add this to the angle already calc’ed for normal pursuit and you have a very passable lead for a intercept . Resample it every once in a while to correct it and you are done. Since these ships do not do quick and radical changes in direction and speed also the distances are rather small, real precision is not needed.

Prediction of end point or of turning is not needed . . just some addtional sampleing