An Alternating Crank-Nicolson Method for Decoupling the Ginzburg-Landau Equations

The time-dependent Ginzburg-Landau model of superconductors consists of coupled nonlinear partial differential equations, which presents difficulties in the numerical solution. We present an alternating Crank-Nicolson method for this model that leads to two decoupled algebraic subsystems; one is linear and the other is semilinear. Both have nice numerical properties and can be solved by efficient matrix solvers. We show the stability and convergence and derive error estimates for this scheme. Numerical results are also reported.