Projected explicit and implicit Taylor series methods for DAEs

Abstract The recently developed new algorithm for computing consistent initial values and Taylor coefficients DAEs using projector-based constrained optimization opens possibilities to apply series integration methods. In this paper, we show how corresponding projected explicit implicit methods can be adapted of arbitrary index. Owing our formulation as a problem by the derivative array, no description inherent dynamics is necessary, various schemes defined in general framework. particular, address higher-order Padé that stand out due their stability. We further discuss several aspects prototype implemented Python Automatic Differentiation. have been successfully tested on examples arising from multibody systems simulation higher-index DAE benchmark servo-constraint problems.