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Abstract only: Solving linear differential equations by using descent

Authors:

Tingting Fang,

Mark van HoeijAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 44, Issue 1/2

Page 26

https://doi.org/10.1145/1838599.1838618

Published: 29 July 2010 Publication History

Abstract

For second order linear ordinary differential equations with coefficients in C(x), we present an algorithm to reduce, whenever possible, the equation to an equation defined over a subfield of C(x). At the moment, we have implemented 2-descent, which means that if there exists a reduction to a subfield of index 2, then we can find it. If n is the number of true singularities, then 2-descent, if it exists, reduces the number of true singularities to at most n/2 + 2. In 12 out of the 17 examples sent to us by Bostan and Kauers, we found that repeated use of 2-descent reduced their regular singular equation down to 3 singularities, which means that 2-descent allows us to find 2F1-hypergeometric type solutions for about two third's of their equations.

Index Terms

Abstract only: Solving linear differential equations by using descent
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 44, Issue 1/2

March/June 2010

77 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/1838599

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 July 2010

Published in SIGSAM-CCA Volume 44, Issue 1/2

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An operator-difference scheme for abstract Cauchy problems

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An operator-difference scheme for abstract Cauchy problems

Numerical solution of retarded functional differential equations as abstract Cauchy problems

On implicit abstract neutral nonlinear differential equations

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