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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the analytic solution of the Cauchy problem
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by Xiang-dong Hou PDF
Proc. Amer. Math. Soc. 137 (2009), 597-606 Request permission

Abstract:

Derivatives of a solution of an ODE Cauchy problem can be computed inductively using the Faà di Bruno formula. In this paper, we exhibit a noninductive formula for these derivatives. At the heart of this formula is a combinatorial problem, which is solved in this paper. We also give a more tractable form of the Magnus expansion for the solution of a homogeneous linear ODE.
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Additional Information
  • Xiang-dong Hou
  • Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
  • Email: xhou@math.usf.edu
  • Received by editor(s): April 13, 2007
  • Received by editor(s) in revised form: January 24, 2008
  • Published electronically: August 22, 2008
  • Communicated by: Jim Haglund
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 597-606
  • MSC (2000): Primary 34A25, 05A15
  • DOI: https://doi.org/10.1090/S0002-9939-08-09493-8
  • MathSciNet review: 2448581