Reduction and completion algorithms for partial differential equations

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Reduction and completion algorithms for partial differential equations

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International Conference on Symbolic and Algebraic Computation archive
Papers from the international symposium on Symbolic and algebraic computation table of contents

Berkeley, California, United States

Pages: 49 - 56

Year of Publication: 1992

ISBN:0-89791-489-9

Author

Fritz Schwarz

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 13, Citation Count: 8

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Ch. Riquier, Les syst~mes d'dquations aux ddrivdes parlielles, Gauthier-Villars, Paris, 1910.
	2	M. Janet, Lecons sur les syst~mes dYquations aux ddrivdes partielles, Gauthier-Villars, Paris, 1929.
	3	F. Schwarz, The Riquier-janet Theory and its Applications to Nonhnear Evolution Equations, Physica 11D, 243-251(1984)
	4	B. Buchberger, Griibner Bases: An Algorithmic Method ~n Polynomial Ideal Theory in Multidimensional Systems Theory, N. K. Bose, ed., Reidel Publisihing Company, 1985.
	5	E. Kamke, Differen~ialgleichungen, LSsungs- methoden und LSsungen. L GewShnliche Differentialgleichungen. Akademische Verlagsgesellschaft, Leipzig, 1962.
	6	Fritz Schwarz, Monomial orderings and Gro¨bner bases, ACM SIGSAM Bulletin, v.25 n.1, p.10-23, Jan. 1991 [doi>10.1145/122525.122526]
	7	F. Schwarz, Term Orderings for Partial Derivatives, to appear.
	8	N. Zabusky and M. Kruskal, Interaction of Solitons in a Collisionless Plasma and the Recurrence of the Initial State, Physical Review Letters 15,240-244 (1965).
	9	F. Schwarz, An Algorithm for Determining the Size of Symmetry Groups, to appear.
	10	F. Schwarz, Symmetries of Differential Equations: From Sophus Lze to Computer Algebra, SIAM Review 30,450-481(1988).
	11	W. Ames, Nonlinear Partial Differential Equations, Academic Press, volume i, 1970, volume II, 1980.

CITED BY 8

	G. J. Reid , I. G. Lisle , A. Boulton , A. D. Wittkopf, Algorithmic determination of commutation relations for Lie symmetry algebras of PDEs, Papers from the international symposium on Symbolic and algebraic computation, p.63-68, July 27-29, 1992, Berkeley, California, United States
	I. G. Lisle , G. J. Reid , A. Boulton, Algorithmic determination of structure of infinite Lie pseudogroups of symmetries of PDEs, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.1-6, July 10-12, 1995, Montreal, Quebec, Canada
	Volker Weispfenning, Differential term-orders, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.245-253, July 06-08, 1993, Kiev, Ukraine
	Gregory J. Reid , Allan D. Wittkopf, Determination of maximal symmetry groups of classes of differential equations, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.272-280, July 2000, St. Andrews, Scotland
	C. J. Rust , G. J. Reid, Rankings of partial derivatives, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.9-16, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Toshinori Oaku, Algorithms for finding the structure of solutions of a system of linear partial differential equations, Proceedings of the international symposium on Symbolic and algebraic computation, p.216-223, July 20-22, 1994, Oxford, United Kingdom
	Ziming Li , Fritz Schwarz , Serguei P. Tsarev, Factoring systems of linear PDEs with finite-dimensional solution spaces, Journal of Symbolic Computation, v.36 n.3-4, p.443-471, September 2003
	Ziming Li , Fritz Schwarz , Serguei P. Tsarev, Factoring zero-dimensional ideals of linear partial differential operators, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.168-175, July 07-10, 2002, Lille, France