On the computation of impasse points of quasi-lineard ifferential-algebraice quations

Mathematics of Computation

Volumn 62, Issue 205, 1994, Pages 133-154

  Rabier, Patrick J ^a   Rheinboldt, Werner C ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84968464929     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1994-1208224-6     Document Type: Article

References (17)

1. R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, tensor analysis and applications, 2nd ed., Springer-Verlag, New York, 1988.
2. R. P. Brent, Some efficient algorithms for solving systems of nonlinear equations, SIAM J. Numer. Anal. 10 (1973), 327-344.
3. K. E. Brennan, S. L. Campbell, and L. R. Petzold, Numerical solution of initial-value problems in differential-algebraic equations, North-Holland, New York, 1989.
4. G. D. Byrne and A. C. Hindmarsh, Stiff ODE solvers: A review of current and coming attractions, J. Comput. Phys. 70 (1987), 1-62.
5. L. O. Chua, Introduction to nonlinear networks, McGraw-Hill, New York, 1969.
6. L. O. Chua and A. C. Deng, Impasse points. Part I: Numerical aspects, Internat. J. Circuit Theory Appl. 17 (1989), 213-235.
7. E. Hairer, C. Lubich, and M. Roche, The numerical solution of differential-algebraic systems by Runge-Kutta methods, Lecture Notes in Math., vol. 1409, Springer-Verlag, New York, 1989.
8. F. A. Potra and W. C. Rheinboldt, Differential-geometric techniques for solving differential-algebraic equations, Real-Time Integration Methods for Mechanical System Simulation (E. J. Haug and R. C. Deyo, eds.), Springer-Verlag, New York, 1991, pp. 155-192.
9. P. J. Rabier, Implicit differential equations near a singular point, J. Math. Anal. Appl. 144 (1989), 425-449.
10. P. J. Rabier and W. C. Rheinboldt, A general existence and uniqueness theory for implicit differential-algebraic equations, J. Differential Integral Equations 4 (1991), 563-582.
11. P. J. Rabier, A geometric treatment of implicit differential-algebraic equations, Tech. Report TR-ICMA-162, Inst. Comput. Math. Appl., Univ. of Pittsburgh, June 1991; J. Differential Equations (in press).
12. P. J. Rabier, On impasse points of quasilinear differential-algebraic equations, Tech. Report TR-ICMA-171, Inst. Comput. Math. Appl., Univ. of Pittsburgh, April 1992; J. Math. Anal. Appl. (in press).
13. W. C. Rheinboldt, Numerical analysis of parametrized nonlinear equations, Wiley, New York, 1986.
14. W. C. Rheinboldt, On the computation of multi-dimensional solution manifolds of parametrized equations, Numer. Math. 53 (1988), 165-181.
15. W. C. Rheinboldt, On the existence and uniqueness of solutions of nonlinear semi-implicit differentialalgebraic equations, J. Nonlinear Anal. TMA 16 (1991), 647-661.
16. G. W. Stewart, Introduction to matrix computations, Academic Press, New York, 1973.
17. F. Takens, Constrained equations: A study of implicit differential equations and their discontinuous solutions, Lecture Notes in Math., vol. 525, Springer-Verlag, New York, 1976, pp. 143-234.