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 κ, 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.