Differential-algebraic systems, their applications and solutions

Byrne, Stiff ODE solvers: a review ofcurrent and coming attractions., J. Comput. Phys, 70, 1987 Byrne, 1983 Caracotsios, 359365, Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations, Comput. chem. Engng., 9, 1985 Douglas, 1970, The numerical solution of a composition model in petroleum reservoir engineering, II, 54 Gear, 1971 Gear, 8995, Simultaneous numerical solution of differential algebraic equations, IEEE Trans. Circuit Theory, CT-18, 1971b Gear, 716728, ODE methods for the solution of differential algebraic systems, SIAM J. Numer. Anal., 21, 1984 Hachtel, 101113, The sparse tableau approach to network analysis and design, IEEE Trans. Circuit Theory, CT-18, 1971 Hindmarsh, 1011, LSODE and LSODI two new initial value ordinary differential equation solvers, ACM SIGNUM Newslett., 15, 1980 Leaf, 1977 Lötedt, 1983 Löstedt, 491516, Numerical solution of nonlinear differential equations with the algebraic constraints Part 1: convergence results for backward differentiation formulae, Math. Comput., 49, 1986 720733, Part 2: practical implications, SIAM J. Sci. Stalist. Comput., 7, 1986 Peaceman, 1977 Petzold, 367384, Differential/algebraic equations are not ODEs, SIAM J. Sci. Slat. Comput., 3, 1982a Petzold L. R. A description of DASSL: a difrerentialalgebraic system solver. Sandia National Laboratory Report SAND82-8637 1982, 1, 65 Petzold, 1986, Numerical methods for differential/algebraic systems, 1986 ODE Conf., Albuquerque