A new family of partitioned Runge-Kutta methods for a special type of differential-algebraic systems

For integration of differential-algebraic systems many integrators have been developed which are perfect for small systems. However, most of these integrators cannot be used to solve systems with several thousands of unknows, as they e.g. occur in viscoplasticity. We present a new family of RUNGE-KUTTA methods optimized for a special type of DAEs, give examples of methods up to order three and apply them to the problem of viscoplasticity using unified viscoplastic models.