Circuit simulation is a standard task in the computer-aided design of electronic circuits. The generation of the circuit equations leads to differential-algebraic equations (DAE). Oscillatory circuits present a special task in the field of circuit simulation. They are important e.g. for radio technology, analog-to-digital conversion and as clock signals in microprocessors. With respect to the analysis of the oscillatory circuits, periodic solutions are of major interest. To avoid the expansive transient integration of numerous periods, direct methods are utilized to approximate the limit cycles. A specialized shooting method for solving the associated boundary-value problem of the differential-algebraic network equations is presented.