Is an Arduino/PI strong/good enough for my application or do I need custom hardware?
(too long for a comment)

First, as @sweber says, you'll have to calculate your real requirements: how much calculations, and at which frequency. With those figures in hand you can make a choice. 

Within the Arduino's there is plenty of variation, from the lowly 8-bit Uno to the 32-bit Due to monsters that run Linux on the side. 

As for a Pi: a Pi with Linux might not be a good idea for a real-time system: the Linux kernel and other processes might get in the way at unpredictable moments. But you can use a Pi bare-metal, and it is a fast beast. But this is not done very often, so you won't find much assistance for it on the web.

So it's back to work for you: create the simulation, use it to get the numbers, then you can make a decision.