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In 2019, the Event Horizon Telescope captured the very first image of a supermassive black hole in center of galaxy Messier 87 (M87*). In the image you observe a black disk in the center, which contains the black hole, and an orange ring surrounding it, which represents an accretion disk. An accretion disk is a flattened structure composed of matter (e.g. gas, dust plasma) found in orbital motion around a massive, gravitating object. Due to gravity, friction, and possibly other forces, it leads to matter gradually spiraling inwards towards the object. This infalling of matter onto the central object is called accretion. In astronomy, we typically observe these accretion disks around compact objects, which are very dense objects formed from the remains of a dying star. A neutron star is one known example of such a compact object. In this thesis, we investigated how the accretion of matter onto the surface of neutron stars affects their spin parameter, which is a dimensionless parameter that depends on their angular momentum and mass, and is a value between 0 and 1. Static neutron stars have a spin parameter equal to zero, while rapidly rotating neutron star have a spin parameter closer to one. Depending on how matter accretes onto the surface of the neutron star, we expect the neutron star to speed up or slow down, which results in the spin parameter to evolve in time. By changing the initial conditions of both the neutron star and the matter orbiting around it, we expect the evolution of the spin parameter to vary between different scenarios. The way how we investigated the evolution of the spin parameter during the accretion process is by simulating an accretion disk around a neutron star. This can be achieved using the recently developed accretion code GMUNU, which is specially designed to numerically solve both Einstein’s equations in General Relativity and the hydrodynamic equations. This code is different from most existing accretion codes because they use a specific approach that involves only solving the latter equations. However, if want more realistic results, we should solve them both simultaneously. We concluded that non-rotating accretion disk models had the biggest impact on slowing down both slow and fast rotating neutron stars. Additionally, when a disk rotates uniformly in the opposite direction to a fast spinning neutron star, it results in a greater increase of the spin parameter compared to the other rotating disk models considered in the simulations.