Timeline for Solution of an ODE upon singular perturbation
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Feb 27, 2023 at 9:55 | history | bounty ended | AndreaPaco | ||
| S Feb 27, 2023 at 9:55 | history | notice removed | AndreaPaco | ||
| Feb 27, 2023 at 9:55 | vote | accept | AndreaPaco | ||
| Feb 23, 2023 at 22:43 | vote | accept | AndreaPaco | ||
| Feb 23, 2023 at 22:43 | |||||
| Feb 21, 2023 at 9:18 | answer | added | cs89 | timeline score: 2 | |
| S Feb 20, 2023 at 22:39 | history | bounty started | AndreaPaco | ||
| S Feb 20, 2023 at 22:39 | history | notice added | AndreaPaco | Authoritative reference needed | |
| Feb 16, 2023 at 10:11 | history | edited | Denis Serre | CC BY-SA 4.0 |
added 13 characters in body
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| Feb 16, 2023 at 10:01 | comment | added | AndreaPaco | @MichaelEngelhardt, I've added to my post that one may want to assume that "the initial velocities of the 2nd-order problem deviate only little from the fixed initial velocities of the 1st order problem", as you suggested. | |
| Feb 16, 2023 at 10:00 | history | edited | AndreaPaco | CC BY-SA 4.0 |
Introduced a possible assumption that one may want to make, as suggested by a comment.
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| Feb 16, 2023 at 9:25 | comment | added | AndreaPaco | Yes, indeed the physics comment is just a sidebar. I see your point about the need of switching to a relativistic description for $M=0$. In any case, this issue goes beyond the purpose of my original question. | |
| Feb 16, 2023 at 2:00 | comment | added | Michael Engelhardt | Certainly, the physics comment is just a sidebar, the main question is how to set up a perturbation scheme of the described type. Physically, a massless particle is inherently relativistic, but the l.h.s. $M \ddot{r} $ in your equation of motion, in which, I guess, you simply set $M=0$, is nonrelativistic. The ostensible solution $v=0$ for $M=0$ is spurious - only solutions with $v=c$ are physical for $M=0$. | |
| Feb 15, 2023 at 19:33 | comment | added | AndreaPaco | @MichaelEngelhardt, thank you for your comment. Why do you say that the massless equation which I wrote isn't actually correct? In any case, I am not particularly interested to the case of massless/massive particles, but on the general way (if any) to approach and solve this kind of problems. | |
| Feb 15, 2023 at 3:40 | comment | added | Michael Engelhardt | Since you invoke physics to motivate the question, I'd just remark that the massless equation you write isn't actually the correct equation of motion of a massless charge in a magnetic field. | |
| Feb 14, 2023 at 4:55 | comment | added | Michael Engelhardt | As you note, the 1st order problem fixes the initial velocities, so for the 1st order problem to be a viable approximation for the 2nd order problem, you at the very least would also have to stipulate that the initial velocities of the 2nd order problem deviate only little from the fixed initial velocities of the 1st order problem, in addition to stipulating that $M$ be small. Perhaps looking at the $N=1$ problem would give some initial conceptual insight? There, the 1st order problem only has the trivial solution $v=0$, which also is a particular solution to the 2nd order problem ... | |
| Feb 13, 2023 at 15:49 | history | asked | AndreaPaco | CC BY-SA 4.0 |