Solving a dynamic traffic assignment problem in a transportation network is a computational challenge. This study first reviews the different algorithms in the literature used to numerically calculate the User Equilibrium (UE) related to dynamic network loading. Most of them are based on iterative methods to solve a fixed-point problem. Two elements must be computed: the path set and the optimal path flow distribution between all origin-destination pairs. In a generic framework these two steps are referred to as the outer and the inner loops, respectively. The goal of this study is to assess the computational performance of the inner loop methods that calculate the path flow distribution for different network settings (mainly network size and demand levels). Several improvements are also proposed to speed up convergence: four new swapping algorithms and two new methods for the step size initialization used in each descent iteration. All these extensions significantly reduce the number of iterations to obtain a good convergence rate and drastically speed up the overall simulations. The results show that the performance of different components of the solution algorithm is sensitive to the network size and saturation. Finally, the best algorithms and settings are identified for all network sizes with particular attention being given to the largest scale.