Skip to main content
SpringerLink
Log in
Book cover

Physik und Informatik — Informatik und Physik pp 318–326Cite as

Formale Theorie partieller Differentialgleichungen

  • Conference paper

  • 96 Accesses

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 306))

Zusammenfassung

Ein klassisches Problem der angewandten Mathematik von großer praktischer Bedeutung liegt in der Berechnung der allgemeinen Lösung einer Differentialgleichung. Mit dem Aufkommen der Computeralgebra erfuhr diese Aufgabe noch eine Verschärfung: Die Konstruktion der Lösung soll algorithmisch erfolgen. Diese Forderung erweist sich jedoch als zu stark, so daß man sich mit geringeren Zielen zufrieden geben muß.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. G.W. Bluman, S. Kumei: Symmetries and Differential Equations. Applied Mathematical Sciences 81, Springer, New York 1989

    Book  MATH  Google Scholar 

  2. G. Carrà Ferro: Gröbner Bases and Differential Algebra. In. Proc. AAECC-5, L. Huguet, A. Poli (Eds.), Lecture Notes in Computer Science 350, Springer, Berlin 1987, S. 129–140

    Google Scholar 

  3. E. Cartan: Sur la Theorié des Systémes en Involution et ses Applications à la Relativité. In. Oeuvres Complètes d’Elie Cartan, Partie II, Vol. 2, Gauthier-Villais, Paris 1953, S. 1199— 1230 (Orginal: Bull. Soc. Math. France 59 (1931) 88–118)

    Google Scholar 

  4. J.H. Davenport, Y. Siret, E. Tournier: Computer Algebra. Academic Press, London 1988

    MATH  Google Scholar 

  5. J. Della Dora, E. Tournier: Formal Solutions of Differential Equations in the Neighbourhood of Singular Points. In. Proc. SYMSAC ’81, P.S. Wang (Ed.), ACM, New York 1981, S. 25–29

    Google Scholar 

  6. J. Denef, L. Lipshitz: Power Series Solutions of Algebraic Differential Equations. Math. Ann. 267 (1984)

    Google Scholar 

  7. A.S. Fokas: Symmetries and Integrability. Stud. Appl. Math. 77 (1987) 253–299

    MathSciNet  MATH  Google Scholar 

  8. E.L. Ince: Ordinary Differential Equations. Dover, New York 1956

    Google Scholar 

  9. I. Kaplansky: An Introduction to Differential Algebra. Hermann, Paris 1957

    MATH  Google Scholar 

  10. E.R. Kolchin: Differential Algebra and Algebraic Groups. Academic Press, New York 1973

    MATH  Google Scholar 

  11. J.J. Kovačic: An Algorithm for Solving Second Order Linear Homogeneous Differential Equations. J. Symb. Comp. 2 (1986) 3–43

    Article  MATH  Google Scholar 

  12. S. Lie, G. Sheffers: Vorlesungen über Continuierliche Gruppen. Teubner, Leipzig 1893

    Google Scholar 

  13. W. Miller: Mechanisms for Variable Separation in Partial Differential Equations and their Relationship to Group Theory. In. Symmetries and Nonlinear Phenomena, D. Levi, P. Winternitz (Eds.), World Scientific, Singapur 1988, S. 188–221

    Google Scholar 

  14. P.J. Olver: Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics 107, Springer, New York 1986

    Book  MATH  Google Scholar 

  15. J.E. Pommaret: Systems of Partial Differential Equations and Lie Pseudogroups. Gordon & Breach, London 1978

    MATH  Google Scholar 

  16. J.F. Pommaret: Differential Galois Theory. Gordon & Breach, London 1983

    MATH  Google Scholar 

  17. J.F. Pommaret, A. Haddak: Effective Methods for Systems of Algebraic Partial Differential Equations. In. Proc. MEGA ’90, T. Mora, C. Traverso (Eds.), Birkhäuser, Boston 1991, S. 411–426

    Google Scholar 

  18. B.D. Saunders: An Implementation of Kovačic’s Algorithm for Solving Second Order Linear Homogeneous Differential Equations. In. Proc. SYMSAC ’81, P.S. Wang (Ed.), ACM, New York 1981, S. 105–108

    Google Scholar 

  19. D.J. Saunders: The Geometry of Jet Bundles. London Mathematical Society Lecture Notes Series 142, Cambridge University Press, Cambridge 1989

    Book  MATH  Google Scholar 

  20. M.F. Singer: Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations. Am. J. Math. 103 (1981) 661–682

    Article  MATH  Google Scholar 

  21. M.F. Singer: Formal Solutions of Differential Equations. J. Symb. Comp. 10 (1990) 59–94

    Article  MATH  Google Scholar 

  22. T. Tsujishita: Formal Geometry of Systems of Differential Equations. Sugaku Expositions 3 (1990) 25–73

    MATH  Google Scholar 

  23. F. Ulmer: On Liouvillian Solutions of Linear Differential Equations. Erscheint in. Appl. Alg. Eng. Comm. Comp.

    Google Scholar 

  24. A.M. Vinogradov: The.-Spectral Sequence, Langrangian Formalism, and Conservation Laws. I. The Linear Theory. II. The Nonlinear Theory. J. Math. Anal. Appl. 100 (1984) 1–40, 41–129

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Weiss, M. Tabor, G. Carnevale: The Painlevé Property for Partial Differential Equations. J. Math. Phys. 24 (1983) 522–526

    Article  MathSciNet  MATH  Google Scholar 

  26. T. Wolf: A Package for the Analytic Investigation and Exact Solution of Differential Equations. In. Proc. EUROCAL ’87, J.H. Davenport (Ed.), Lecture Notes in Computer Science 378, Springer, Berlin 1987, S. 479–490

    Google Scholar 

  27. Wu W.-T.: A Constructive Theory of Differential Algebraic Geometry based on works of J.F. Ritt with Particular Applications to Mechanical Theorem Proving of Differential Geometries. In. Proc. Differential Geometry and Differential Equations, Shanghai 1985, G. Chaohao, M. Berger, R.L. Bryant (Eds.), Lecture Notes in Mathematics 1255, Springer, Berlin 1987, S. 173–189

    Google Scholar 

  28. Wu W.-T.: Automatic Derivation of Newton’s Gravitational Laws from Kepler’s Laws. In. Academica Sinica Mathematics-Mechanization Research Preprints 1 (1987) 53

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Universität Karlsruhe, 7500, Karlsruhe 1, Deutschland

    Werner M. Seiler

Authors
  1. Werner M. Seiler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dornier GmbH, Postfach 1420, W-7990, Friedrichshafen 1, Deutschland

    D. Krönig

  2. Lehrstuhl für Elektroakustik, Technische Universität München, Arcisstr. 21, W-8000, München 2, Deutschland

    M. Lang

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Seiler, W.M. (1992). Formale Theorie partieller Differentialgleichungen. In: Krönig, D., Lang, M. (eds) Physik und Informatik — Informatik und Physik. Informatik-Fachberichte, vol 306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77382-2_40

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77382-2_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55298-7

  • Online ISBN: 978-3-642-77382-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation