A Fast Semi-Implicit Finite Difference Method for the TDGL Equations

We propose a finite-difference algorithm for solving the time-dependent Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for intermediate values of the Ginzburg-Landau parameter $\kappa$, allows time-steps two orders of magnitude larger than commonly used in explicit schemes. We demonstrate the use of the method by solving a fully three-dimensional problem of a current-carrying wire with longitudinal and transverse magnetic fields.