In this manuscript we present our experience of porting the code used in the wave-packet convergent-close-coupling (WP-CCC) approach to NVIDIA V100 and AMD MI250X GPUs. The WP-CCC approach is used in the field of ion-atom collision physics to describe various processes such as elastic scattering, target excitation and electron-capture by the projectile. It effectively models collisions between proton or bare ion projectiles and various atomic and molecular targets, particularly those resembling one or two-electron systems. These calculations are used in computational atomic physics, fusion plasma modeling, and hadron therapy for cancer treatment. The main computational cost of the method is solving a set of coupled first-order differential equations. This involves implementing the standard Runge-Kutta method while varying the projectile position along multiple straight-line paths. At each projectile position several millions of matrix elements need to be calculated which is accomplished using the OpenACC programming model. After computing these matrix elements, the next steps involve matrix inversion and multiplication with another matrix. To expedite these operations, a GPU-accelerated LAPACK routine, specialised for solving systems of linear equations, is employed. For AMD GPUs, this routine is accessible through the hipSOLVER library, while for NVIDIA GPUs, it can be obtained from the cuSOLVER library. The portability, performance and energy efficiency of the CPU-only code have been compared with the GPU-accelerated version running on AMD and NVIDIA GPUs. The implementation of GPU-accelerated WP-CCC code opens up avenues for exploring more sophisticated collision processes involving complex projectile and target structures, which were previously considered infeasible.