Sweeping algorithms for inverting the discrete Ginzburg-Landau operator (Q1208327)

The author considers the problem of the solution of the Ginzburg-Landau equations in superconductivity. He discusses a method of discretization of the equations and suggests a form of numerical solution similar to the shooting technique for ordinary differential equations. Partial sweeping and iterative algorithms are discussed, and the possibility of using techniques such as ``divide and conquer'' and alternating directions. He points out that solutions of the finite difference system can involve highly ill-conditioned matrices. The paper is very largely descriptive.