The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees

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The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees

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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: 89 - 94

Year of Publication: 1992

ISBN:0-89791-489-9

Authors

P. E. Crouch
R. L. Grossman

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

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Downloads (6 Weeks): 0, Downloads (12 Months): 17, Citation Count: 1

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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.

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	2	j. C. Butcher, The Numerical Analysis of Or&- navy Differential Equations, John Wiley, 1986.
	3	A. Cayley, "On the theory of the analytical forms called trees," in Collected Mathematical Papers of Arthur Cayley, Cambridge Univ. Press, Cambridge, 1890, Vol. 3, pp. 242-246.
	4	A. Cayley, "On the analytical forms called trees. Second part," in Collected Mathematical Papers ofArlhur Cayley, Cambridge Univ. Press, Cambridge, 1891, Vol. 4, pp. 112-115.
	5	A. Chorin, T. J. R. Hughes, J. E. Marsden, and M. McCracken, "Product Formulas and Numerical Algorithms," Comm. Pure and Appl. Math., Vol. 31, pp. 205-256, 1978.
	6	Guoting Chen , Jean Della Dora , Laurent Stolovitch, Nilpotent normal form via Carleman linearization (for systems of ordinary differential equations), Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.281-288, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120737]
	7	P. E. Crouch and R. L. Grossman, "Numerical integration of ordinary differential equations on manifolds," submitted to Journal of Nonlinear Science.
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	9	Peter Crouch , Robert Grossman , Richard Larson, Computations involving differential operators and their actions on functions, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.301-307, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120740]
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	14	P. Leroux and X. G. Viennot, "Combinatorial resolution of systems of differential equations, I: Ordinary differential equations," in Combinatoire Enumerative, UQAM 1985, Proceedings, Lecture Notes in Mathematics, Volume 1234, Springer-Verlag, 1986, pp. 210-245.
	15	P. Leroux , G. X. Viennot, Combinatorial resolution of systems of differential equations. IV. Separation of variables, Discrete Mathematics, v.72 n.1-3, p.237-250, December 1988 [doi>10.1016/0012-365X(88)90213-0]
	16	P. Leroux and X. G. Viennot, "A combinatorial approach to nonlinear functional expansions," 27lh Conference on Decision and Control, Austin, Texas, pp. 1314-1319, 1988.
	17	Fritz Schwarz, Existence theorems for polynomial first integrals, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.256-264, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120733]