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Collection of papers related to Kovacic algorithm for solving differential equations

Nasser M. Abbasi

June 1, 2021   Compiled on June 1, 2021 at 2:21am

Contents

1 The papers
 1.1 An Algorithm for Solving Second Order Linear Homogeneous Differential Equations (1985 version)
 1.2 An Algorithm for Solving Second Order Linear Homogeneous Differential Equations (2005 version)
 1.3 An Implementation of Kovacic’s Algorithm for Solving Second Order Linear Homogeneous Differential Equations
 1.4 A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS
 1.5 Kovacic’s Algorithm and Its Application to Some Families of Special Functions
 1.6 Note on Kovacic’s Algorithm
 1.7 Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Differential Equations
 1.8 How to Solve Linear Differential Equations: An Outline
 1.9 Solving Second Order Linear Differential Equations with Klein’s Theorem
 1.10 Liouvillian solutions for second order linear differential equations with polynomial coefficients
 1.11 A rationality result for Kovacic’s algorithm
 1.12 NonLiouvillian Solutions for Second Order Linear ODEs
 1.13 Galois Groups of Second and Third Order Linear Differential Equations
 1.14 Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations
 1.15 Algorithm implementation in FriCAS
  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.

Chapter 1
The papers

1.1 An Algorithm for Solving Second Order Linear Homogeneous Differential Equations (1985 version)

This is the original paper by JERALD J. KOVACIC.

1.2 An Algorithm for Solving Second Order Linear Homogeneous Differential Equations (2005 version)

By JERALD J. KOVACIC.

1.3 An Implementation of Kovacic’s Algorithm for Solving Second Order Linear Homogeneous Differential Equations

By B. David Saunders

1.4 A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

By Carolyn J. Smith.

1.5 Kovacic’s Algorithm and Its Application to Some Families of Special Functions

By Anne Duval, and Michele Loday-Richaud.

1.6 Note on Kovacic’s Algorithm

By FELIX ULMER and JACQUES-ARTHUR WEIL

1.7 Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Differential Equations

By FELIX ULMER and Michael F. Singer.

1.8 How to Solve Linear Differential Equations: An Outline

By FELIX ULMER

1.9 Solving Second Order Linear Differential Equations with Klein’s Theorem

By Mark van Hoeij, Jacques-Arthur Weil and Thomas Cluzeau.

1.10 Liouvillian solutions for second order linear differential equations with polynomial coefficients

By Primitivo B. Acosta‑Humánez, David Blázquez‑Sanz, Henock Venegas‑Gómez

1.11 A rationality result for Kovacic’s algorithm

By Marius van der Put, Peter A. Hendriks

1.12 NonLiouvillian Solutions for Second Order Linear ODEs

By L. Chan, E.S. Cheb-Terrab

1.13 Galois Groups of Second and Third Order Linear Differential Equations

By MICHAEL F. SINGER and FELIX ULMER. Journal of Symbolic Computation, 16, July 1993, 9 - 36

1.14 Liouvillian and Algebraic Solutions of Second and Third Order Linear Differential Equations

By MICHAEL F. SINGER and FELIX ULMER. Journal of Symbolic Computation, 16, July 1993, 37 - 74.

1.15 Algorithm implementation in FriCAS

See https://github.com/fricas/fricas/blob/master/src/algebra/kovacic.spad