  In the present paper we develop an algorithm to solve the time dependent
Ginzburg-Landau (TDGL) equations, by using the link variables technique, for
circular geometries. In addition, we evaluate the Helmholtz and Gibbs free
energy, the magnetization, and the number of vortices. This algorithm is
applied to a circular sector. We evaluate the superconduting-normal magnetic
field transition, the magnetization, and the superconducting density.
Furthermore, we study the nucleation of giant and multi-vortex states for that
geometry.
