Study and Solution of the Ginzburg-Landau Equation for Superconductivity Problems

Abstract

This work focuses on the study and numerical solution of the Ginzburg-Landau (hereafter referred to as GL) partial differential equation, which models the behavior of superconducting materials. Depending on its parameters, the Ginzburg-Landau model can exhibit chaotic states that are challenging to approximate numerically, requiring the use of high-order numerical schemes. In this work, the resolution of this model was addressed in both the 1D and 2D cases. In both cases, an IMEX-type method based on finite differences was used, which provided good results.