Abstract In this contribution, we show the implementation of the Link-variable method for solve the complete set of acopled non-linear time dependent Ginzburg-Landau differential equations in a three-dimensional homogeneous and isotropic mesoscopic superconducting system. In this case, the sample is immersed in an external magnetic d at zero applied current. The effects of demagnetization are taken in count and we show the order parameter and its phase in zero field cooling and field cooling process. This numerical analysis shows good results when this solution is applied to a superconducting cubic sample.