A splitting integrator for the BCS equations of superconductivity

The BCS equations are the centerpiece of the microscopic description of superconductivity. Their space discretization yields a system of coupled ordinary differential equations. In this work, we come up with fast time evolution schemes based on a splitting approach. One of the schemes only requires basic operations. For the physically important case of the BCS equations for a contact interaction potential, the computational cost of the schemes increases only linearly with the dimension of the space discretization. Their accuracy is demonstrated in extensive numerical experiments. These experiments also show that the physical energy of the system is preserve up to very small errors.