Parallel iterative algorithms are computing methods in which the communications can be synchronized or not at the end of each iteration. When the convergence is slow, in synchronous parallel iterative algorithms, given a heterogeneous distributed architecture, the idle times of the processing units will degrade the performance and elapsed times will be penalized. In asynchronous parallel iterative algorithms, the calculations are processed on each processor respecting the own rhythm of each processing unit and using the last available values calculated by the other processors. So, the advantage lies in the fact that there is generally a reduction in the elapsed time to reach convergence. In previous studies these methods were implemented on grids constituted by heterogeneous and distant machines and asynchronous algorithms were very efficient when there was lots of synchronizations between the processors. This talk investigates the implementation of these two kinds of methods and their comparison on a Cloud computing architecture with several sizes of algebraic systems derived from the discretization of linear boundary values problem to be solved. It can be noticed that, in this context and for the resolution of linear classical boundary values problems, the asynchronous computation scheme gives better results than the synchronous scheme.