Fortunately, we're dealing with much shorter distances here. Relativistic physics need not concern us overly much 
The example I gave was something like 20% longer than the distance from the earth to the sun. Are you dealing with millions of km, thousands, or what?
Well, planning the acceleration and deceleration on a 50-50 base is fine if the target doesn't do anything, but everyone's moving around! Bastards! So the ideal turnover point might actually shift around!
Could I still calculate that point by some handy formula, or does this transgress into mathematics too advanced for us to handle? 
Well, again, are you trying to ram the target, or board it?
If ramming, then you don't really need a turnover point. The idea is to hit turnover right in the enemy ship's engine room, with as much velocity as possible
Bonus points for delivering a greeting card from Sir Isaac Newton.
But with a target whose position, velocity, or even acceleration are not constant, things do get more complicated, as it requires prediction of where the target
will be at a given time, and ifguring out if you can be there at that time.
And if those changes to target position, velocity, or acceleration are not even
known beforehand, then obviously you cannot generate a guaranteed solution at all.
At that point, what you can do is plot a sort of conical volume showing all possible points where the target
could be after x seconds. Then it's a matter of plotting your course and acceleration such that "your cone" envelops "their cone" (for the section up to time T, where T is the longest time it would take you to reach any point within that section), with an actual course heading that will generate a collision on the target's most likely actual course. Then just recompute that course every time there's any alteration in the target's acceleration or heading, etc. Of course, if you
can't find a course an acceleration that give you that kind of envelopment, then the target ship is capable of evading you regardless of how you fly (whether or not they actually
would evade you is up to them).
But this is probably only feasible with relatively low accelerations, and the ability to change headings relatively fast (not overcoming momentum in the old direction quickly, but generating momentum in the new direction quickly). If you've got ships that can pull 100,000 gravities or whatever then those cones might look more like spheres and I'm not sure what impact that would have on the practical value of the technique.
On the other hand, if you're actually trying for something like a zero-zero intercept with the evading target then... um, shoot its engines out?
More seriously, you're going to want some way of predicting the target's location, velocity, and accel (as in the case of forming up with a friendly target) OR some way of disabling the target's ability to change its accel and heading OR some way to "grapple" the enemy ship (or tractor beam it, or whatever) once you're close enough. Or I guess maybe you just have to get within weapons range and make it so there's no target to get close to anymore.
But the basic idea is similar to the ramming case, you basically check for that conical area overlap and do a full burn towards the target, but periodically check "if I engage full decel now, how far will I go before I reach zero velocity?" and when that number is >= "my remaining distance to target", engage full decel. And then potentially keep re-checking to see if the target putting on more accel or whatever makes it so that you want to start accelerating again.
Anyway, I think the basic solution to "but what if the situation keeps changing?" is "then re-run the math every time the situation changes"
Or every time it's changed enough to be significant, etc.
In terms of concrete distances, velocities, accelerations, and objectives (least-time vs zero-zero, i.e. ramming vs boarding), can you give me an example of what you're trying to do?
