On the resolution of singularities of ordinary differential systems

Numerical Algorithms

Volumn 19, Issue 1-4, 1998, Pages 247-259

  Tuomela, Jukka ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Differential equations; Jet spaces; Singularities

Indexed keywords

EID: 0043225105     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1019179128548     Document Type: Article

References (19)

1. V. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Grundlehren, Vol. 250 (Springer, 1983).
2. 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).
3. U. Ascher and P. Lin, Sequential regularization methods for nonlinear higher index DAEs, to appear in SIAM J. Sci. Comput.
4. K. Brenan, S. Campbell and L. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (North-Holland, 1989).
5. D. Cox, J. Little and D. O'Shea, Ideals, Varieties and Algorithms, Undergraduate Texts Math. (Springer, 1992).
6. H. Goldschmidt, Integrability criteria for systems of non-linear partial differential equations, J. Differential Geom. 1 (1967) 269-307.
7. É. Goursat, Cours d'Analyse Mathématique, Vol. 2, 6th ed. (Gauthier-Villars, 1942).
8. G.-M. Greuel, G. Pfister and H. Schönemann, SINGULAR Version 1.2 User Manual, Reports On Computer Algebra, No. 21, Centre for Computer Algebra, University of Kaiserslautern (June 1998); http://www.mathematik.uni-kl.de/∼zca/Singular.
9. J. Harris, Algebraic Geometry, Graduate Texts Math., Vol. 133 (Springer, 1992).
10. E. Hubert, Étude algébrique et algoritmique des singularités des équations différentielles implicites, Ph.D. thesis, Institut National Polytechnique Grenoble (1997).
11. I. Kaplansky, An Introduction to Differential Algebra (Hermann, 1957).
12. J.F. Pommaret, Differential Galois Theory, Math. Appl., Vol. 15 (Gordon and Breach, 1983).
13. J.F. Ritt, Differential Algebra, Amer. Math. Soc. Colloq. Publ., Vol. 33 (Amer. Math. Soc., Providence, RI, 1950; Dover, 1966).
14. D. Saunders, The Geometry of Jet Bundles, London Math. Soc. Lecture Note Ser., Vol. 142 (Cambridge University Press, 1989).
15. D. Spencer, Overdetermined systems of linear partial differential equations, Bull. Amer. Math. Soc. 75 (1969) 179-239.
16. M. Spivak, A Comprehensive Introduction to Differential Geometry, Vols. 1-5, 2nd ed. (Publish or Perish, 1979).
17. J. Tuomela, On singular points of quasilinear differential and differential-algebraic equations, BIT 37 (1997) 966-975.
18. J. Tuomela, On the numerical solution of involutive ordinary differential systems: Higher order methods, Research Report A397, Helsinki University of Technology (1998).
19. J. Tuomela and T. Arponen, On the numerical solution of involutive ordinary differential systems: Introduction and numerical results, Research Report A393, Helsinki University of Technology (1998).