Timeline for (Non-) Convergence of solutions in a family of linear ODE's
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2020 at 9:45 | vote | accept | Stefan Perko | ||
| Nov 23, 2020 at 17:12 | answer | added | Loïc Teyssier | timeline score: 2 | |
| Nov 19, 2020 at 8:28 | comment | added | Stefan Perko | @LoïcTeyssier I'm still very interested in your answer - if you like to write one, no pressure. | |
| Nov 16, 2020 at 11:44 | comment | added | Stefan Perko | @LoïcTeyssier Do you have any readings you can point me to? I'm not familiar with singular points or the passage to the complex domain in this context (I haven't studied ODE's all that much). | |
| Nov 16, 2020 at 11:43 | comment | added | Stefan Perko | @LoïcTeyssier Yeah, I know I ignored the coefficient $C_d$ - mostly because in the original problem I was actually looking for $\int y$ and then there was an argument for $d = 0$ that let you conclude that $C_0 = 0$. I wanted to extend this somehow to the $d > 0$ case (which doesn't seem possible anymore), so I thought it could be a little bit sloppy in my explanation without serious harm. | |
| Nov 16, 2020 at 11:12 | comment | added | Loïc Teyssier | Also as $d\to 0$ you have a merging of two regular (=simple) singular points into an irregular (=multiple) singular point (in the complex line). This kind of bifurcation can be wild sometimes. Try looking into the complex domain to have convergence. | |
| Nov 16, 2020 at 11:07 | comment | added | Loïc Teyssier | There is no reason why your particular choice of $f_d$ should converge towards $f_0$, you must take into account the coefficient $C_d$ to built a converging family of solutions starting from a given (fixed) initial value. | |
| Nov 16, 2020 at 10:29 | history | asked | Stefan Perko | CC BY-SA 4.0 |