We draw a comparison between two numerical methods to solve a magnetostatic problem set on a bounded convex domain. The problem is of vector Poisson type and is associated with boundary conditions set on the curl of the unknown, here the magnetic field. These boundary conditions therefore introduce a coupling between the components. One of the two algorithms under consideration consists in an adaptation of the influence matrix method introduced by R. Glowinski and O. Pironneau on the biharmonic equation and extended later by L. Quartapelle and coworkers. We present a detailed description of the practical implementation of the algorithm. Through various numerical tests, we compare this uncoupled method with a strategy consisting of a direct attack of the coupled problem.