Timeline for Optimal ODE method for fixed number of RHS evaluations
Current License: CC BY-SA 3.0
7 events
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| May 22, 2013 at 14:13 | comment | added | Florian Brucker | @WolfgangBangerth: $N$ is relatively small, see my updated question. | |
| May 22, 2013 at 13:50 | comment | added | Wolfgang Bangerth | @FlorianBrucker: What I think isn't quite clear is whether the same methods that we know work well for asymptotically large $N$ are also the best for small $N$, say $N<1000$. In other words, you need to tell us something about your budget in terms of how many function evaluations you can afford. | |
| May 22, 2013 at 13:48 | comment | added | Wolfgang Bangerth | @FlorianBrucker I think I may have misunderstood your question. It's not that you don't care about function evaluations but that you say the number of function evaluations is bounded. I guess then the question is: Is $N$ large or small? Because the development of ODE solvers has been guided by minimizing $N$ keeping the error constant for decades, and at least for asymptotically large $N$ we know the best methods: high order methods (e.g. RK45) with adaptive time stepping. For these, it is also clear that the larger $N$ the smaller the error. | |
| May 22, 2013 at 7:11 | comment | added | Florian Brucker | @DavidKetcheson: This is not the case here. It's rather that we have very strict timing requirements (hard real-time) on weak hardware (embedded devices). The ODE systems themselves are comparatively small. | |
| May 22, 2013 at 7:02 | comment | added | Florian Brucker |
Can you please explain how this relates to my question? I don't see the connection, since I'm interested in the case where evaluating f(x) is not free but rather so expensive that the number of evaluations is limited.
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| May 22, 2013 at 6:44 | comment | added | David Ketcheson | +1. Whenever somebody asks about efficient ODE solvers, I just assume they're interested in huge systems of ODEs coming from PDE semi-discretizations or large n-body problems. | |
| May 22, 2013 at 5:19 | history | answered | Wolfgang Bangerth | CC BY-SA 3.0 |