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

Author

Listed:
  • Juan Tang

    (School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China)

  • Jianguang Lu

    (State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China
    Chongqing Innovation Center of Industrial Big-Data Co., Ltd., Chongqing 400707, China)

Abstract

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.

Suggested Citation

  • Juan Tang & Jianguang Lu, 2023. "Modified Extended Lie-Group Method for Hessenberg Differential Algebraic Equations with Index-3," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2360-:d:1150535
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