Theory of formal integrability and DAEs: effective computations

1. F. Boulier, Etude et implémentation de quelques algorithmes en algèbre différentielle, Ph.D. thesis, Université des Sciences et Technologies de Lille (1994).

2. F. Boulier, D. Lazard, F. Ollivier and M. Petitot, Representation for the radical of a finitely generated differential ideal, in: Proc. of ISSAC' 95, Montréal, ed. T. Levelt (ACM Press, New York, 1995) pp. 158-166.

   Google Scholar 

3. T. Becker and V. Weispfenning, Gröbner Bases, a Computational Approach to Commutative Algebra, Graduate Texts in Mathematics 141 (Springer, Berlin, 1993).

   MATH  Google Scholar 

4. S.L. Campbell, The numerical solution of higher index linear time varying singular systems of differential equations, SIAM J. Sci. Statist. Comput. 6 (1988) 334-348.

   Article  Google Scholar 

5. S.L. Campbell and C.W. Gear, The index of general nonlinear DAEs, J. Numer. Math. 72(2) (1995) 173-196.

   Article  MATH  MathSciNet  Google Scholar 

6. C.W. Gear, Differential-algebraic equations index transformations, SIAM J. Sci. Statist. Comput. 9 (1988) 39-47.

   Article  MATH  MathSciNet  Google Scholar 

7. H. Goldschmidt, Existence theorems for analytic linear PDEs, Ann. Math. 86 (1962) 246-270.

   Article  MathSciNet  Google Scholar 

8. M. Kuranishi, On E. Cartan's prolongation theorem of exterior differential systems, Amer. J. Math. 79 (1957) 1-47.

   Article  MATH  MathSciNet  Google Scholar 

9. D. Lazard, Letter (November 1996).

10. Y.O. Macutan, Geometry of differential equations and formal integrability theory, Technical Report RT170, LMC-IMAG, Grenoble (1997).

    Google Scholar 

11. B. Malgrange, Equations de Lie II, J. Differential Geom. 7 (1972) 117-141.

    MATH  MathSciNet  Google Scholar 

12. O.-P. Piirilä, J. Tuomela and G. LeVey, Differential-algebraic systems and formal integrability, Research Report A326, Helsinki University of Technology (1993).

13. M.-P. Quéré and G. Villard, An algorithm for the reduction of linear DAE, in: Proc. of ISSAC' 95, ed. A.H.M. Levelt (ACM Press, New York, 1995) pp. 223-231.

    Google Scholar 

14. P.J. Rabier, Implicit differential equations near a singular point, J. Math. Anal. Appl. 144 (1988) 425-449.

    Article  MathSciNet  Google Scholar 

15. P.J. Rabier and W.C. Rheinboldt, A geometric treatment of implicit differential-algebraic equations, J. Differential Equations 109 (1994) 110-146.

    Article  MATH  MathSciNet  Google Scholar 

16. P.J. Rabier and W.C. Rheinboldt, On impasse points of quasilinear differential-algebraic equations, J. Math. Anal. Appl. 181 2 (1994) 429-454.

    Article  MATH  MathSciNet  Google Scholar 

17. S. Reich, On an existence and uniqueness theory for nonlinear differential-algebraic equations, Circuits Systems Signal Process. 10(3) (1991) 343-359.

    Article  MATH  MathSciNet  Google Scholar 

18. G.J. Reid, P. Lin and A.D. Wittkopf, Differential elimination-completion algorithms for DAE and PDAE, preprint (1996).

19. J.F. Ritt, Differential Algebra (Amer. Mathematical Soc., Providence, RI, 1950).

    MATH  Google Scholar 

20. D.C. Spencer, Overdetermined systems of linear partial differential equations, Bull. Amer. Math. Soc. 75 (1965) 1-114.

    Google Scholar 

21. G. Thomas, Symbolic computation of the differential index of quasi-linear DAEs, in: ACM Proc. of ISSAC' 96, ed. Y. Lakshmann (ETH, Zürich, 1996) pp. 196-203.

    Google Scholar 

22. G. Thomas, Contributions à l'étude des équations différentielles-algébriques: Approche par le calcul formel, Thèse INP, Grenoble (1997).

    Google Scholar 

23. J. Tuomela, On singular points of quasilinear differential and differential-algebraic equations, preprint, Institute of Mathematics, Helsinki University of Technology (1996).

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