Something I've said before, when this same question gets asked...
If you will do heavy computations for lengthy periods of time, you will find your CPU gets hot. And I mean, literally hot. Enough so that it can cook the innards. And that means it needs to cool itself down. If your system does not have a good fan (laptops do not seems to have good fans in my experience, if they have any fan at all) then it needs to artificaially slow itself down. It does this by changing its clock speed. It talks in ssssssllllooooowwwww motion.
When this was a problem for us, and we were using a laptop as our only choice, we got an external fan, so a fan the laptop sat on top of. And that did help, a lot. Better, if you are doing heavy duty computations, and you have a choice, is to use a stationary system, with a GOOD internal fan! The result be be full speed, all the time. No throttling needed.
As for any other specifications, that very much depends on what you are doing. For example, some problems cannot be easily parallelized. And that means you don't need lots of cores on your CPU, but you do need a CPU with high clock speed. For example, large scale symbolic computations generally use only one core. But if you are doing massive linear algebra, then lots of cores will help. And large scale linear algebra happens for many problems. Solving large scale NONLINEAR systems of equations? It still uses linear algebra internally. Solving an ODE with thousands of equartions? Large scale. So you need to know what class of problems you are solving before you decide on the optimal system. Of course, if you just get lots of memory and the fasted possible cpu that you can afford, it is a good start.
You mention numerical integration of differential equations, but we don't know what is taking the time there. Is this just a very large problem? Again, now linear algebra is important then.
