Numerical solution of nonlinear differential equations with algebraic constraints i: Convergence results for backward differentiation formulas

Mathematics of Computation

Volumn 46, Issue 174, 1986, Pages 491-516

  Petzold, Linda ^b  

^a SAAB AB   (Sweden)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966252011     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0829621-X     Document Type: Article

References (28)

1. A. BEN-ISRAEL and T. N. E. Greville, Generalized Inverses: Theory and Applications, Wiley, New York, 1974.
2. F. H. BRANIN, "Computer methods of network analysis, " Proc. IEE-E, v. 55, 1967, pp. 1787-1801.
3. F. H. BRANIN,. , "The network concept as a unifying principie in engineering and the physical sciences, " in Problem Analysis in Science and Engineering (F. H. Branin, Jr. and K. Huseyin, eds.), Academic Press, New York, 1977.
4. K. BRENAN, Stability and Convergence of Différence Approximations for Higher Index Differential-Algebraic Systems with Applications in Trajectory Control, Ph. D. Thesis, University of California at Los Angeles, 1983.
5. D. A. Calahan, Computer-Aided Network Design, rev. ed., McGraw-Hill, New York, 1972.
6. S. L. CAMPBELL, "The numerical solution of higher index linear time varying singular systems of differential équations, " SI AM J. Sci. Statist. Comput., v. 6, 1985, pp. 334-348.
7. S. L. CAMPBELL, Explicit Methods for Solving Singular Differential Equation Systems, North Carolina State University, Raleigh, North Carolina, 1984. (Preprint.)
8. S. L. Campbell, Singular Systems of Differential Equations, Pitman, San Francisco, 1979.
9. S. L. Campbell & L. R. Petzold, "Canonical forms and solvable singular systems of differential équations, " SI AM J. Algebraic Discrète Methods, v. 4, 1983, pp. 517-521.
10. R. W. COTTLE, "Manifestations of the Schur complément, " Linear Algebra Appl., v. 8, 1974, pp. 189-211.
11. R. Courant & K. O. Friedrichs, Supersonic Flow and Shock Waves, Springer-Verlag, Berlin and New York, 1948.
12. J. DIEUDONNE, Foundations of Modem Analysis, Academic Press, New York, 1969.
13. C. W. Gear, "Simultaneous numerical solution of differential/algebraic équations, " IEEE Trans. Circuit Theory, CT-18, 1971, pp. 89-95.
14. C. W. Gear & L. R. Petzold, "ODE methods for the solution of differential/algebraic systems, " SI AM J. Numer. Anal., v. 21, no. 4, 1984, pp. 367-384.
15. P. M. GRESHO, R. L. LEE & R. L. SANI, "On the time-dependent solution of the incompressible Navier-Stokes équations in two and three dimensions, " Recent Advances in Numerical Methods in Fluids, vol. 1, Pineridge, Swansea, 1980.
16. P. M. GRESHO & C. D. UPSON, Current Progress in Solving the Time-Dépendent, Incompressible Navier-Stokes Equations in Three-Dimensions by (Atmost) the FEM, UCRL-87445, Lawrence Livermore National Laboratory, Livermore, California, 1982.
17. G. D. HACHTEL, R. K. BRAYTON & F. G. GUSTAVSON, "The sparse tableau approach to network analysis and deisgn, " IEEE Trans. Circuit Theory, CT-18, 1971, pp. 101-113.
18. P. Henrici, Error Propagation for Différence Methods, Wiley, New York, 1963.
19. E. S. KUH & R. A. ROHRER, "The state-variable approach to network analysis, " Proc. IEE-E, v. 53, 1965, pp. 672-686.
20. W. LINIGER, "Multistep and one-leg methods for implicit mixed differential algebraic systems, " IEEE Trans. Circuits and Systems, CAS-26, 1979, pp. 755-762.
21. P. LÖTSTEDT, "Mechanical systems of rigid bodies subject to unilateral constraints, " SIAM J. Appl. Math"v. 42, 1982, pp. 281-296.
22. P. LÖTSTEDT & L. R. PETZOLD, Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints, SAND 83-8877, Sandia National Laboratories, Livermore, California, 1983.
23. J. F. PAINTER, Solving the Navier-Stokes Equations with LSODI and the Method of Lines, Report UCID-19262, Lawrence Livermore National Laboratory, Livermore, California, 1981.
24. B. PAUL, "Analytical dynamics of mechanisms-A computer oriented overview, " Mech. Mach. Theory, v. 10, 1975, pp. 481-507.
25. L. PETZOLD, "Differential/algebraic équations are not ODEs, " SIAM J. Sci. Statist. Comput., v. 3, no. 3, 1982, pp. 367-384.
26. L. R. PETZOLD & P. LÖTSTEDT, "Numerical solution of nonlinear differential équations with algebraic constraints II: Practical implications, " SIAM J. Sci. Statist. Comput. (To appear.)
27. R. F. SINCOVEC, B. DEMBART, M. A. EPTON, A. M. ERISMAN, J. W. MANKE & E. L.YIP, Solvability of Ixirge-Scale Descriptor Systems, Report, Boeing Computer Services Company, Seattle, Washington, 1979.
28. J. WITTENBURG, Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart, 1977.