Linear ordinary differential equations

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Linear ordinary differential equations: breaking through the order 2 barrier

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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: 42 - 48

Year of Publication: 1992

ISBN:0-89791-489-9

Author

Manuel Bronstein

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): 4, Downloads (12 Months): 21, Citation Count: 14

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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	S. A. Abramov, Rational solutions of linear differential and difference equations with polynomial coefficients, USSR Computational Mathematics and Mathematical Physics, v.29 n.6, p.7-12, 1989 [doi>10.1016/S0041-5553(89)80002-3]
	2	S. A. Abramov , K. Yu. Kvansenko, Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.267-270, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120735]
	3	Manuel Bronstein, The Risch differential equation on an algebraic curve, Proceedings of the 1991 international symposium on Symbolic and algebraic computation, p.241-246, July 15-17, 1991, Bonn, West Germany [doi>10.1145/120694.120731]
	4	Manuel Bronstein, On solutions of linear ordinary differential equations in their coefficient field, Journal of Symbolic Computation, v.13 n.4, p.413-439, April 1992 [doi>10.1016/S0747-7171(08)80106-X]
	5	E. Kamke, Differentialgleichungen, Lb'sungmethoden und Lb'sungen, L GewShnhche Differentzalgleichungen, Akad. Verlag., Leipzig, 1959.
	6	Jerald J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, Journal of Symbolic Computation, v.2 n.1, p.3-43, March 1986 [doi>10.1006/jsco.1998.0266]
	7	F. Schwarz, A factorization algorithm for linear ordinary differential equations, Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation, p.17-25, July 17-19, 1989, Portland, Oregon, United States [doi>10.1145/74540.74544]
	8	M.F. Singer, Liouvillian Solutions of nth Order Homogeneous Linear Differential Equations, American Journal of Mathematics, 103, No. 4, pp. 661- 682 (1981).
	9	Michael F. Singer, Liouvillian solutions of linear differential equations with Liouvillian coefficients, Journal of Symbolic Computation, v.11 n.3, p.251-273, March 1991 [doi>10.1016/S0747-7171(08)80048-X]
	10	M.F. Singer & F. Ulmer, Bounds and Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Differential Equations, manuscript 1992, abstract in these proceedings,
	11	C. Smith, A Discussion and Implementation of Kovacic's Algorithm for Ordinary Differential Equations, Res. Report CS 84-35, Dpt. of Computer Science, Univ. of Waterloo, Ontario, 1984.
	12	E. Tournier, Solutions Formelles d'Equations Diff&entielles, Thee d%tat, IMAG, Grenoble, 1987.

CITED BY 14

	Marius van der Put , Peter A. Hendriks, A rationality result for Kovacic's algorithm, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.4-8, July 06-08, 1993, Kiev, Ukraine
	Mark van Hoeij, Rational solutions of the mixed differential equation and its application to factorization of differential operators, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.219-225, July 24-26, 1996, Zurich, Switzerland
	Jacques-Arthur Weil, The use of the special semi-groups for solving differential equations, Proceedings of the international symposium on Symbolic and algebraic computation, p.341-347, July 20-22, 1994, Oxford, United Kingdom
	Eckhard Pflügel, An algorithm for computing exponential solutions of first order linear differential systems, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.164-171, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Sergei A. Abramov , Marko Petkovšek, D'Alembertian solutions of linear differential and difference equations, Proceedings of the international symposium on Symbolic and algebraic computation, p.169-174, July 20-22, 1994, Oxford, United Kingdom
	Manuel Bronstein, An improved algorithm for factoring linear ordinary differential operators, Proceedings of the international symposium on Symbolic and algebraic computation, p.336-340, July 20-22, 1994, Oxford, United Kingdom
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003
	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
	Reinhold Burger , George Labahn , Mark van Hoeij, Closed form solutions of linear odes having elliptic function coefficients, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.58-64, July 04-07, 2004, Santander, Spain
	S. A. Abramov, On d'Alembert substitution, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, p.20-26, July 06-08, 1993, Kiev, Ukraine
	George Labahn , Ziming Li, Hyperexponential solutions of finite-rank ideals in orthogonal ore rings, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.213-220, July 04-07, 2004, Santander, Spain
	Ruyong Feng , Xiao-shan Gao, Rational general solutions of algebraic ordinary differential equations, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.155-162, July 04-07, 2004, Santander, Spain
	Fritz Schwarz, Efficient factorization of linear ODE's, ACM SIGSAM Bulletin, v.28 n.1, p.9-17, March 1994
	Ziming Li , Michael F. Singer , Min Wu , Dabin Zheng, A recursive method for determining the one-dimensional submodules of Laurent-Ore modules, Proceedings of the 2006 international symposium on Symbolic and algebraic computation, July 09-12, 2006, Genoa, Italy