## On the analytic solution of the Cauchy problem

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- by Xiang-dong Hou PDF
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**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.## 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
- 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