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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the analytic solution of the Cauchy problem

Author(s): Xiang-dong Hou
Journal: Proc. Amer. Math. Soc. 137 (2009), 597-606.
MSC (2000): Primary 34A25, 05A15
Posted: August 22, 2008
MathSciNet review: 2448581
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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.

References:

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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

DOI: 10.1090/S0002-9939-08-09493-8
PII: S 0002-9939(08)09493-8
Keywords: Cauchy problem, ODE, Magnus expansion, partial order, combinatorics, Bruno's formula
Received by editor(s): April 13, 2007,
Received by editor(s) in revised form: January 24, 2008
Posted: August 22, 2008
Communicated by: Jim Haglund
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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