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Collection of papers related to Kovacic algorithm for
solving diﬀerential equations
December 31, 2020 Compiled on December 31, 2020 at 7:17am
These are collection of papers related to Kovacic algorithm for solving diﬀerential equations. As
I was studying the algorithm, I thought it will be good to have any related paper I ﬁnd on the
subject in one place for easy access. The HTML version has only the outlines. Only the PDF
version has the actual papers shown.
1.1 An Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations
This is the original paper by JERALD J. KOVACIC.
1.2 An Implementation of Kovacic’s Algorithm for Solving Second Order Linear Homogeneous
By B. David Saunders
1.3 A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR
ORDINARY DIFFERENTIAL EQUATIONS
By Carolyn J. Smith.
1.4 Kovacic’s Algorithm and Its Application to Some Families of Special Functions
By Anne Duval, and Michele Loday-Richaud.
1.5 Note on Kovacic’s Algorithm
By FELIX ULMER and JACQUES-ARTHUR WEIL
1.6 Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Diﬀerential
By FELIX ULMER and Michael F. Singer.
1.7 How to Solve Linear Diﬀerential Equations: An Outline
By FELIX ULMER
1.8 Solving Second Order Linear Diﬀerential Equations with Klein’s Theorem
By Mark van Hoeij, Jacques-Arthur Weil and Thomas Cluzeau.
1.9 Liouvillian solutions for second order linear diﬀerential equations with polynomial
By Primitivo B. Acosta‑Humánez, David Blázquez‑Sanz, Henock Venegas‑Gómez
1.10 A rationality result for Kovacic’s algorithm
By Marius van der Put, Peter A. Hendriks
1.11 NonLiouvillian Solutions for Second Order Linear ODEs
By L. Chan, E.S. Cheb-Terrab