Timeline for Behavior of a non-linear differential equation
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 8, 2018 at 10:42 | answer | added | user539887 | timeline score: 2 | |
| Apr 4, 2018 at 3:23 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Apr 4, 2018 at 2:54 | vote | accept | Ludwig | ||
| Apr 4, 2018 at 2:39 | review | Close votes | |||
| Apr 4, 2018 at 9:09 | |||||
| Apr 4, 2018 at 1:57 | comment | added | Gerhard Paseman | He presents the error as 1/a*a times something. Since b could be as big as a (we don't know if it is being held constant ) I see it as 1/a times x times some geometric series like thing varying with x. So I do not see it as (hold b and hold x, and let a get big). That plus the oscillation of r is how I see it. Gerhard "It's A Matter Of Perspective" Paseman, 2018.04.03. | |
| Apr 4, 2018 at 1:02 | comment | added | Ludwig | @GerhardPaseman: Robert Israel's answer looks correct to me. So could you please elaborate your thoughts? | |
| Apr 4, 2018 at 0:28 | comment | added | Gerhard Paseman | I normally don't challenge a post of Robert Israel, because he does quality work. I suspect his O terms in this case and think a different conclusion should be reached. When I derive an equation for r from your problem, I find r has a derivative that is near -b sin(at), and thus r oscillates without substantial decay, even as a grows large. Gerhard "I'm Seeing More Of Nonzero" Paseman, 2018.04.03. | |
| Apr 4, 2018 at 0:17 | comment | added | Ludwig | @GerhardPaseman: I do not know what the "exact" form of the term $r(a,t)$ is. I guessed its limiting behavior for $a\to \infty$ on the basis of some numerical evidences. (And, of course, my guess could be wrong) | |
| Apr 4, 2018 at 0:09 | comment | added | Gerhard Paseman | Did you try writing x in the desired form and plugging it into the equation? I don't see how you could then reach your conclusion of r going to zero. Gerhard "The Derivative Changes Too Much" Paseman, 2018.04.03. | |
| Apr 3, 2018 at 23:47 | comment | added | Ludwig | @RobertIsrael: You are right, thanks! I've just edited my question according to your comments. | |
| Apr 3, 2018 at 23:46 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Apr 3, 2018 at 23:45 | answer | added | Robert Israel | timeline score: 4 | |
| Apr 3, 2018 at 23:40 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Apr 3, 2018 at 23:35 | comment | added | Robert Israel | "The" solution? There are infinitely many, unless you set an initial condition. Do you mean "some solution", or "every solution" instead of "the solution"? Also, if $|a| \le |b|$ all solutions are bounded. Do you mean to restrict to the case $a > |b|$? | |
| Apr 3, 2018 at 22:28 | history | edited | Ludwig | CC BY-SA 3.0 |
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| Apr 3, 2018 at 22:28 | comment | added | Piotr Hajlasz | The questions does not seem obvious to me. Unless you know it is a standard result in ODE's don't vote it down. | |
| Apr 3, 2018 at 22:20 | comment | added | Ludwig | I believe that my question is a research-level one, so I don’t understand why it received a downvote. Anyway, if the MO community think this is not actually the case, could someone please migrate it to MSE in order to avoid cross-postings? Thanks! | |
| Apr 3, 2018 at 21:47 | history | asked | Ludwig | CC BY-SA 3.0 |