Evidence of an unknown planet in our solar system?

Yes, they use computation of possibilities :

'... we carry out comprehensive N−body simulations that self-consistently model gravitational perturbations from all giant planets, the Galactic tide, as well as passing stars, stemming from initial conditions that account for the primordial giant planet migration and sun’s early evolution within a star cluster'

S

Cheers, Mike.

Short answer : Yes they are similar, but no you can't use their results. Each N-body simulation is different in the number of bodies and the so-called initial conditions plus some other stuff.

Long Answer : N-body simulation is a general idea rather than a specific technique. The idea is that the gravitational force law is expressed in terms of two bodies (let's assume they are using Newton's Law of Gravity or some expression derived from that). Now if you only have two bodies in your simulation the mathematics is the simplest, the orbits are all 'conic sections' : circles, ellipses, parabolas, hyperbolas etc, depending on the total energy in the system. Now if you put in even a single extra body (ie. N>2) you can no longer solve the equations in 'closed form', put another way there is no neat mathematical function that describes the situation. But one can solve for the evolution of the system - where are all the bodies and how are they moving - by simulation or mathematical approximation. This is a time step method and each body is assumed to move according to some average influence over a short enough interval. To mitigate the errors of approximation the time steps may vary and the whole situation is subject to checks so that conservation laws (energy, momentum, angular momentum) are upheld. But this explanation is too simple (& dated) to describe what they actually do. There are a lot of references in the paper to earlier studies that have dealt with the methodology. It seems quite a refined, and arcane, field of study so that if Planet Nine is verified as a true finding then the methods are also validated.

Cheers, Mike. 

If there is significant evidence (or probabilities) for a Planet Nine, scientists should quickly find an appropriate Roman name for it, while there is still plenty of time to think and consider.