On singular points of quasilinear differential and differential-algebraic equations

BIT Numerical Mathematics

Volumn 37, Issue 4, 1997, Pages 968-977

  Tuomela, Jukka ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Impasse points; Implicit differential equations; Singular differential equations

Indexed keywords

EID: 0000091956     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510364     Document Type: Article

References (18)

1. V. Arnold, A. Varchenko, and S. Goussein-Zadé, Singularités des Applications Différentiables I: Classification des Points Critiques, des Caustiques et des Fronts d'Onde, Mir, 1986.
2. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, 1989.
3. L. Chua and A. Deng, Impasse points. Part I: numerical aspects, Int. J. Circuit Theory Appl., 17 (1989), pp. 213-235.
4. L. Chua and A. Deng, Impasse points. Part II: analytical aspects, Int. J. Circuit Theory Appl., 17 (1989), pp. 271-282.
5. E. Hairer, C. Lubich, and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, vol. 1409, Springer, 1989.
6. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer Series in Comp. Math., vol. 14, Springer, 1991.
7. R. März, Numerical methods for differential-algebraic equations, Acta Numerica, 1 (1992), pp. 141-198.
8. K. Murota, Structural approach in systems analysis by mixed matrices, an exposition for index of DAE, in Proceedings of ICIAM 95, K. Kirchgässner, O. Mahrenholtz, and R. Mennicken, eds., Akademie Verlag, 1996, pp. 257-279.
9. P. Rabier, Implicit differential equations near a singular point, J. Math. Anal. Appl., 144 (1989), pp. 425-449.
10. P. Rabier and W. Rheinboldt, On impasse points of quasilinear differential algebraic equations, J. Math. Anal. Appl., 181 (1994), pp. 429-454.
11. P. Rabier and W. Rheinboldt, On the computation of impasse points of quasilinear differential algebraic equations, Math. Comp., 62 (1994), pp. 133-154.
12. G. Reissig, Impasse points: examples and counterexamples, Preprint ET-IEE-1, TU Dresden, Fakultät Elektrotechnik, 1993.
13. G. Reissig, Differential-algebraic equations and impasse points, IEEE Trans. Circ. Syst. I, 43 (1996), no. 2, pp. 122-133.
14. M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. 1, 2nd ed., Publish or Perish, 1979.
15. M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. 3, 2nd ed., Publish or Perish, 1979.
16. J. Tuomela, On the numerical solution of involutive ordinary differential systems, Research Report A363, Helsinki University of Technology, 1996.
17. R. Winkler, On simple impasse points and their numerical computation, Preprint 94-15, Institut für Mathematik, Humboldt-Univ. Berlin, 1994.
18. S. Wolfram, Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, 1991.