Future machines such as the electron-ion colliders (JLEIC), linac-ring machines (eRHIC) or LHeC are particularly sensitive to beam-beam effects. This is the limiting factor for long-term stability and high luminosity reach. The complexity of the non-linear dynamics makes it challenging to perform such simulations which require millions of turns. Until recently, most of the methods used linear approximations and/or tracking for a limited number of turns. We have developed a framework which exploits a massively parallel Graphical Processing Units (GPU) architecture to allow for tracking millions of turns in a sympletic way up to an arbitrary order and colliding them at each turn. The code is called GHOST for GPU-accelerated High-Order Symplectic Tracking. As of now, there is no other code in existence that can accurately model the single-particle non-linear dynamics and the beam-beam effect at the same time for a large enough number of turns required to verify the long-term stability of a collider. Our approach relies on a matrix-based arbitrary-order symplectic particle tracking for beam transport and the Bassetti-Erskine approximation for the beam-beam interaction
