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Kovacic algorithm

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1: 31.14 General Fuchsian Equation
§31.14(ii) Kovacic’s Algorithm
An algorithm given in Kovacic (1986) determines if a given (not necessarily Fuchsian) second-order homogeneous linear differential equation with rational coefficients has solutions expressible in finite terms (Liouvillean solutions). … For applications of Kovacic’s algorithm in spatio-temporal dynamics see Rod and Sleeman (1995).
2: 31.8 Solutions via Quadratures
For more details see Smirnov (2002). The solutions in this section are finite-term Liouvillean solutions which can be constructed via Kovacic’s algorithm; see §31.14(ii).
3: Bibliography K
  • J. J. Kovacic (1986) An algorithm for solving second order linear homogeneous differential equations. J. Symbolic Comput. 2 (1), pp. 3–43.