Implicit integration of the TDGL equations of superconductivity
  This article is concerned with the integration of the time-dependent Ginzburg--Landau (TDGL) equations of superconductivity. Four algorithms, ranging from fully explicit to fully implicit, are presented and evaluated for stability, accuracy, and compute time. The benchmark problem for the evaluation is the equilibration of a vortex configuration in a superconductor that is embedded in a thin insulator and subject to an applied magnetic field. 
D. O. Gunter, H. G. Kaper and G. K. Leaf