Timeline for Solve and understand a NDSolve error: Step Size effectively zero; singularity or stiff system suspected
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 12 at 15:01 | comment | added | Michael E2 | @UlrichNeumann You're welcome! :) | |
| Sep 12 at 14:53 | comment | added | Ulrich Neumann | @MichaelE2 I got it, thanks again! | |
| Sep 12 at 14:47 | comment | added | Michael E2 | @UlrichNeumann No, I meant a vertical asymptote. The equilibrium points are on the boundary between the periodic solutions and those that blow up. (Well, except for the one at the origin, of course.) [Sorry, for the constant updates.] The StreamPlot does not really show the asymptotes. | |
| Sep 12 at 14:45 | comment | added | Ulrich Neumann | @MichaelE2 Thanks for your answer. Perhaps I misunderstood what "pole" means. I thought it is an equilibrium point ( green dots in your plotl) | |
| Sep 12 at 14:39 | comment | added | Michael E2 |
@UlrichNeumann '...NDSolve is able to integrate "over" the poles but stops with the stepsize message.' -- I've found none. Once x[t] gets above 10^6 or so, it soon stops with a zero-step-size error. What is an initial condition where NDSolve[] gets over the pole? I'm pretty sure the pole in all cases I've found is of the form $x(t) \sim c\,(t-t_0)^{-1/2}$, where the pole at $t=t_0$ is close to the stopping point.
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| Sep 12 at 7:57 | comment | added | Ulrich Neumann | @MichaelE2 Thank you for answer. I tried several initial conditions , NDSolve is able to integrate "over" the poles but stops with the stepsize message. Additionally, knowing the asymptotic behavior from your fine answer, I tried to transform the ode, unfortunately without success | |
| Sep 10 at 14:30 | comment | added | Michael E2 |
As Bill Watts commented, the solution heads to infinity if you plot it. NDSolve[] can't integrate past a pole, so at some point, the step size must become smaller than the smallest step supported by the floating-point system.
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| Sep 10 at 7:35 | comment | added | Ulrich Neumann | @MichaelE2 That's an interesting solution. To me it is still unclear why the direct numerical solution aborts. Any idea? Thanks! | |
| Sep 10 at 0:36 | comment | added | Michael E2 |
@Felps Perhaps x, v, or t has a value. Try Clear[x, v, t, k, \[Gamma]] and re-executing. The False in place of the equation to be solved in the error message shows something was defined already.
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| Sep 9 at 23:59 | vote | accept | Felps | ||
| Sep 9 at 23:56 | comment | added | Felps |
I tried to run your code, but it went wrong, it gives me the message: Coordinate $CellContextSolveValues[False, {$CellContextx, $CellContextv}, Reals] should be a pair of numbers, or a Scaled or Offset form.. Why is that?
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| Sep 9 at 19:23 | history | edited | Michael E2 | CC BY-SA 4.0 |
Clarification
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| Sep 9 at 11:19 | history | answered | Michael E2 | CC BY-SA 4.0 |