References
- Brenan , K. E. , Campbell , S. L. and Petzold , L. R. 1989 . Numerical Solution of Initial-Value Problems in Differential—algebraic Equations , Amsterdam : North-Holland .
- Deuflhard , P. , Hairer , E. and Zugck , J. 1987 . One-step and extrapolation methods for differential-algebraic systems . Numerical Mathematics , 51 : 501 – 516 .
- Griepentrog , E. and Marz , R. 1986 . Differential–algebraic equations and their Numerical Treatment , Leipzig : Teuner .
- Hairer , E. , Lubich , Ch. and Roche , M. 1989 . “ The numerical solution of differential–algebraic systems by Runge–Kutta methods ” . In Lecture Notes in Mathematics , Vol. 1409 , Berlin : Springer .
- Gear , C. W. 1971 . Simultaneous solution of differential–algebraic equations . IEEE Transactions on Circuit Theory , 18 : 89 – 95 .
- Lötstedt , P. and Petzold , L. 1986 . Numerical solution of nonlinear differential equations with algebraic constraints. I: Convergence results for backward differentiation formulas . SIAM Journal on Scientific and Statistical Computing , 7 : 720 – 733 .
- Marz , V. 1986 . On one-leg methods for differential–algebraic equations . Circuits, Systems and Signal Processing , 5 : 87 – 95 .
- Petzold , L. 1986 . Order results for implicit Runge–Kutta methods applied to differential/algebraic systems . SIAM Journal on Numerical Analysis , 23 : 837 – 852 .
- Roche , M. 1989 . Implicit Runge–Kutta methods for differential–algebraic equations . SIAM Journal on Numerical Analysis , 26 : 963 – 975 .
- Rentrop , P. , Roche , M. and Steinebach , G. 1989 . The application of Rosenbrock–Wanner type methods with stepsize control in differential–algebraic equations . Numerical Mathematics , 55 : 545 – 563 .
- Roche , M. 1988 . Rosenbrock methods for differential–algebraic equations . Numerical Mathematics , 52 : 45 – 63 .
- Çelik , E. , Karaduman , E. and Bayram , M. 2002 . Numerical method to solve chemical differential–algebraic equations . International Journal of Quantum Chemistry , 89 : 447 – 451 .
- Çelik , E. and Bayram , M. 2003 . On the numerical solution of differential–algebraic equations by Padé series . Applied Mathematics and Computations , 137 : 151 – 160 .
- Çelik , E. and Bayram , M. 2005 . The numerical solution of physical problems modeled as systems of differential–algebraic equations (DAEs) . Journal of the Franklin Institute , 342 : 1 – 6 .
- Hindmarsh , A. C. 1980 . LSODE and LSODI: two new initial value ordinary differential equation solvers . ACM–SIGNUM Newsletter , 15 : 10 – 11 .
- Petzold , L. 1983 . “ A description of DASSL: a differential/algebraic system solver ” . In Scientific Computing , Edited by: R.S. , Stepleman . 65 – 68 . Amsterdam : North-Holland .
- Deuflhard , P. and Nowak , U. 1987 . “ Extrapolation integrators for quasilinear implicit ODEs ” . In Large-Scale Scientific Computing , Edited by: Deuflhard , P. and Engquist , B. 37 – 50 . Boston, MA : Birkhauser .
- Hairer , E. and Wanner , G. 1988 . Radau5: An Implicit Runge–Kutta Code , University of Geneva . Report, Department of Mathematics
- Wu , B. and White , R. E. 2001 . An initialization subroutine for DAE solvers: DAEIS . Computers and Chemical Engineering , 25 : 301 – 311 .
- Ascher , U. M. and Petzold , L. R. 1998 . Computer Methods for Ordinary Differential Equations and Differential–Algebraic Equations , Philadelphia, PA : Society for Industrial and Applied Mathematics .