×

Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. (English) Zbl 1034.65066

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.

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

Software:

ADIFOR; DASPK 3.0
PDFBibTeX XMLCite
Full Text: DOI