CHORAL -- a charge-oriented algorithm for the numerical integration of electrical circuits Circuit simulation packages generate the network equations automatically. In time domain analysis this results in a system of differential-algebraic equations that is solved numerically by BDF schemes and/or the trapezoidal rule. CHORAL, a charge-oriented Rosenbrock Wanner method, has been developed as an alternative approach for digital circults. By its successful implementation into TITAN, the circuit simulator of Infineon Technologies, a second integration scheme is available for the first time. Results for benchmarks and industrial circuits show that CHORAL is competitive with the standard ansatz and possesses advantages for oscillatory circuits.