Variable step size time integration methods for transient eddy current problems

For transient eddy current problems modelled as differential-algebraic equations (DAEs), a time integration method suitable for ordinary differential equations (ODEs) will not necessarily work. We present two Runge-Kutta methods that are suitable for the time integration of the classes of DAEs to which eddy current problems belong. Both methods have error estimators and hence allow variable step sizes. In tests our variable step size integrators were competitive with fixed step size integrators, in particular with Crank-Nicolson.