Solving second order linear differential equations via algebraic invariant curves

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The idea to find first integrals for polynomial vector fields via algebraic invariant curves can be traced back to Darboux in the 19th century. In 1983, this approach was further developed by Prelle and Singer to become a semi-decision algorithm for finding elementary first integrals. In this paper, we describe how to extend the Prelle-Singer method to deal with second order linear differential equations via Kovacic’s results on algebraic solutions of Riccati equations. Some illustrative examples on using this approach are provided. Copyright © 2009 Newswood Limited.
Original languageEnglish
Title of host publicationProceedings of the World Congress on Engineering 2009
EditorsS. I. AO, Len GELMAN, David WL HUKINS, Andrew HUNTER, A. M. KORSUNSKY
Place of PublicationLondon, UK
PublisherNewswood Limited
Pages1040-1042
VolumeII
ISBN (Print)9789881821010
Publication statusPublished - 2009

Citation

Man, Y.-K. (2009). Solving second order linear differential equations via algebraic invariant curves. In S. I. Ao, L. Gelman, D. W. L. Hukins, A. Hunter, & A. M. Korsunsky (Eds.), Proceedings of the World Congress on Engineering 2009 (Vol. II, pp. 1040-1042). London, UK: Newswood Limited.

Keywords

  • Algebraic invariant curves
  • The Prelle-Singer method
  • Kovacic’s theorem
  • Riccati equations
  • Second order linear differential equations

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