| Title:
|
Systémy algebro-diferenciálních rovnic (Czech) |
| Title:
|
Systems of differential-algebraic equations (English) |
| Author:
|
Simerská, Carmen |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
182-192 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
constrained differential equation |
| Keyword:
|
numerical method |
| Keyword:
|
systems of differential-algebraic equations |
| MSC:
|
34A09 |
| MSC:
|
65L80 |
| idZBL:
|
Zbl 1265.65148 |
| . |
| Date available:
|
2010-12-11T21:03:50Z |
| Last updated:
|
2015-11-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141270 |
| . |
| Reference:
|
[1] Silverman, L. M.: Inversion of multivariable systems.IEEE Trans. Aut. Control, AC-14 (1969), 270–276. MR 0267927, 10.1109/TAC.1969.1099169 |
| Reference:
|
[2] Luenberger, D. G.: Dynamic equations in descriptor form.IEEE Trans. Aut. Control, AC-22 (1977), 312–321. Zbl 0354.93007, MR 0479482, 10.1109/TAC.1977.1101502 |
| Reference:
|
[3] Gear, C. W.: The simultaneous numerical solution of differential-algebraic equations.IEEE Trans. Circuit Theory, CT-18 (1971), 89–95. 10.1109/TCT.1971.1083221 |
| Reference:
|
[4] Gear, C. W., Petzold, L. R.: ODE methods for the solution of differential/algebraic systems.SIAM J. Numer. Anal. 21 (1984), 716–728. Zbl 0557.65053, MR 0749366, 10.1137/0721048 |
| Reference:
|
[5] Lötstedt, P., Petzold, L.: Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas.Math. Comp. 46 (1986), 491–516. MR 0829621, 10.2307/2007989 |
| Reference:
|
[6] Hairer, E., Lubich, C., Roche, M.: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods.Springer-Verlag, Berlin 1989. Zbl 0683.65050, MR 1027594 |
| Reference:
|
[7] Hairer, E., Lubich, C.: Extrapolation at stiff differential equations.Numer. Math. 52 (1988), 377–400. Zbl 0643.65034, MR 0932706, 10.1007/BF01462235 |
| Reference:
|
[8] Griepentrog, E., Märtz, R.: Differential-Algebraic Equations and Their Numerical Treatment.Teubner, Leipzig 1986. MR 0877350 |
| Reference:
|
[9] Märtz, R.: On initial value problems in differential-algebraic equations and their numerical treatment.Computing 35 (1985), 13–37. MR 0809676, 10.1007/BF02240144 |
| Reference:
|
[10] Hindmarsh, A. C.: LSODE and LSODI, two new initial value ordinary differential equation solvers.ACM-SIGNUM Newsletters 15 (1980), 10–11. 10.1145/1218052.1218054 |
| Reference:
|
[11] Petzold, L. R.: A description of DASSL: a differential-algebraic system solver.In: Scientific Computing, eds. Stepleman et al., North-Holland, Amsterdam 1983, 65–68. MR 0751605 |
| Reference:
|
[12] Brenan, K. E., Campbell, S. L., Petzold, L. R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations.North-Holland, Amsterdam 1989. Zbl 0699.65057, MR 1101809 |
| Reference:
|
[13] Gear, C. W.: Differential-algebraic equations, indices, and integral algebraic equations.SIAM J. Numer. Anal. 27 (1990), 1527–1534. Zbl 0732.65061, MR 1080336, 10.1137/0727089 |
| Reference:
|
[14] Gear, C. W.: Numerical Initial Value Problems in Ordinary Differential Equations.Prentice-Hall, Englewood Cliffs, NJ 1971. MR 0315898 |
| Reference:
|
[15] Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems.Springer-Verlag, Berlin 1991. Zbl 0729.65051, MR 1111480 |
| Reference:
|
[16] Hindmarsh, A., Taylor, A.: User Documentation for IDA: A Differential-Algebraic Equation Solver for Sequential and Parallel Computers.Lawrence Livermore National Laboratory report, UCRL-MA-136910, December 1999. |
| Reference:
|
[17] Reisig, G., Martinson, W. S., Barton, P. I.: Differential-algebraic equations of index $1$ may have an arbitrary high structural index.SIAM J. Scientific Computing (2000), 1987–1990. MR 1762026 |
| Reference:
|
[18] Rabier, P. J., Rheinboldt, W. C.: Theoretical and numerical analysis of differentialālgebraic equations.Handbook of Numerical Analysis VIII, Elsevier Publ., North Holland 2002. MR 1893418 |
| . |
