Timeline for Name of a Frobenius-like method for ODEs
Current License: CC BY-SA 4.0
10 events
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| Jul 12, 2023 at 13:15 | comment | added | Willie Wong | @IgorKhavkine: thank you for the reference! I will check it out later. | |
| Jul 11, 2023 at 21:59 | comment | added | Igor Khavkine | Since a Poincaré asymptotic expansion (power series asympototics) is unique when it exists, the difference between your way of writing it (using $\omega(x)$) and the output of the Frobenius method consists only of lower order terms. In the matter of the expansion itself, I think then credit belongs to Frobenius (analyticity is irrelevant, as all you need are formal power series expansions of everything at the singular point). If you need something like existence by the singular case of Picard's theorem, some classical references are around Sec.3.3 of Erdélyi's Asymptotic Expansions (1956). | |
| Jul 11, 2023 at 14:31 | comment | added | Willie Wong | @IgorKhavkine: no, generally you don't expect this to give you too much of an advantage; but in the specific case, we know the explicit function $\omega$ so it is easier not to take the Taylor series expansion. The intent of this question is pretty much just to give credit if appropriate | |
| Jul 11, 2023 at 14:10 | comment | added | Igor Khavkine | Don't know if this old question is still of interest, but I don't really see an innovative advantage to writing an asymptotic expansion for $v/u_0^2$ in terms of the derivatives of $1/\omega^2(x)$ rather than just replacing that function by its Taylor series and integrating $x^{-2\lambda}/\omega^2(x)$ term by term. Either way, you at most obtain an asymptotic series for $v(x)$ at $x=0$. Knowing the full (or even a sufficiently high order) expansion for $v(x)$, it is possible to construct $v(x)$ by Picard iteration (without analyticity assumptions), cf proof of Thm.17.1 in Wasow. | |
| Jul 10, 2023 at 2:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 12, 2023 at 2:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 10, 2023 at 1:52 | answer | added | Phil Harmsworth | timeline score: 1 | |
| S Feb 8, 2023 at 16:13 | history | suggested | J. W. Tanner |
added terminology tag
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| Feb 8, 2023 at 15:04 | review | Suggested edits | |||
| S Feb 8, 2023 at 16:13 | |||||
| Feb 8, 2023 at 14:42 | history | asked | Willie Wong | CC BY-SA 4.0 |