Cao, Yang; Li, Shengtai; Petzold, Linda; Serban, Radu Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. (English) Zbl 1034.65066 SIAM J. Sci. Comput. 24, No. 3, 1076-1089 (2003). Summary: An adjoint sensitivity method is presented for parameter-dependent differential-algebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system (for fully implicit DAEs) is shown. In addition, it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system. Cited in 67 Documents MSC: 65L80 Numerical methods for differential-algebraic equations 34A09 Implicit ordinary differential equations, differential-algebraic equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:sensitivity analysis; DAE; adjoint method; differential-algebraic equation; system; stability Software:ADIFOR; DASPK 3.0 PDFBibTeX XMLCite \textit{Y. Cao} et al., SIAM J. Sci. Comput. 24, No. 3, 1076--1089 (2003; Zbl 1034.65066) Full Text: DOI