Modified Extended Lie-Group Method for Hessenberg Differential Algebraic Equations with Index-3

Hessenberg differential algebraic equations (Hessenberg-DAEs) with a high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie-group differential algebraic equation (LGDAE) method, which handles index-2 systems, we first propose a modified extended Lie-group differential algebraic equation (MELGDAE) method for solving index-3 Hessenberg-DAEs and then provide a theoretical analysis to deepen the foundation of the MELGDAE method. Moreover, the performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index-2 and -3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits a competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index-3 Hessenberg-DAEs achieve second-order convergence using the MELGDAE method, which suggests the potential for extension to Hessenberg-DAEs with an index of 4 or higher.