$C^r$ convergence of Picard’s successive approximations
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- by Alexander J. Izzo PDF
- Proc. Amer. Math. Soc. 127 (1999), 2059-2063 Request permission
Abstract:
A simple, elementary proof of the existence, uniqueness, and smoothness of solutions to ordinary differential equations is given. In fact, it is shown that for a differential equation of class $C^{r}$, the successive approximations of Picard converge in the $C^{r}$-sense.References
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Additional Information
- Alexander J. Izzo
- Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
- MR Author ID: 307587
- Email: aizzo@math.bgsu.edu
- Received by editor(s): October 6, 1997
- Published electronically: February 26, 1999
- Communicated by: Hal L. Smith
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2059-2063
- MSC (1991): Primary 34A12, 34A45
- DOI: https://doi.org/10.1090/S0002-9939-99-04801-7
- MathSciNet review: 1486736