Manuel Bronstein
- 1.S.A. Abramov, Rational Solutions of Linear Differential and Difference Equations with Polynomzal Coefficients (in russian), Journal of Computational Mathematics and Mathematical Physics, Vol. 29, No.ll, pp. 1611-1620, 1989. Google Scholar
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- 2.S.A. Abramov & K.Yu. Kvashenko, Fast Algorithms for the Search of the Rational Solutions of Linear Differential Equations with Polynomial Coefficients, in "Proceedings of ISSAC '91", Bonn, ACM Press, pp. 267-270, 1991. Google ScholarDigital Library
- 3.M. Bronstein, The Risch Differential Equat,on on an Algebraic Curve, in "Proceedings ofISSAC '91", Bonn, ACM Press, pp. 241-246, 1991. Google ScholarDigital Library
- 4.M. Bronstein, On Solutions of Linear Ordinary Differential Equations in their Coefficient Field, Research Report 152, Informatik, ETH Ziirich, 1991, to appear in the journal of Symbolic Computation. Google ScholarDigital Library
- 5.E. Kamke, Differentialgleichungen, Lb'sungmethoden und Lb'sungen, L GewShnhche Differentzalgleichungen, Akad. Verlag., Leipzig, 1959.Google Scholar
- 6.Kovacic J.J.: An Algorithm for Solving Second Order Linear Homogeneous Differentzal Equatzons, Journal of Symbolic Computation, 2, 3-43 (1986). Google ScholarDigital Library
- 7.F. Schwarz, A Factorisatzon Algorithm for Linear Ordinary Differential Equations, in "Proceedings of ISSAC '89", Portland, ACM Press, pp. 17-25, 1989. Google ScholarDigital Library
- 8.M.F. Singer, Liouvillian Solutions of nth Order Homogeneous Linear Differential Equations, American Journal of Mathematics, 103, No. 4, pp. 661- 682 (1981).Google ScholarCross Ref
- 9.M.F. Singer, Liouvillian Solutions of Linear Differential Equations with Lzouv,llian Coefficients, Journal of Symbolic Computation. 11, pp. 251-273 (1991). Google ScholarDigital Library
- 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,Google Scholar
- 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.Google Scholar
- 12.E. Tournier, Solutions Formelles d'Equations Diff&entielles, Thee d%tat, IMAG, Grenoble, 1987.Google Scholar
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Linear ordinary differential equations: breaking through the order 2 barrier
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