Timeline for How to select initial time step in adaptive time step ODE solver (TR-BDF2)
Current License: CC BY-SA 4.0
11 events
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| Nov 19, 2020 at 9:01 | vote | accept | kostas1335 | ||
| Nov 19, 2020 at 8:35 | comment | added | Laurent90 | Yes this is the spirit. However it may indeed be too pessimist and let you choose an unnecessarily low value of the initial time step. I didn't write it here, but Hairer and Wanner also describe on the same page some "default" behaviour as @ChrisRackauckas mentionned. Lastly, you can also take a the initial time step as a fraction of some characteristic time of your system. | |
| Nov 19, 2020 at 7:45 | comment | added | kostas1335 | @Laurent90 as far as I understand, regardless of whether we are using explicit methods, to derive the initial timestep, the Euler step is used as a rule of thumb, at the risk of being somewhat unstable as it was pointed out above, is that correct? | |
| Nov 19, 2020 at 6:12 | comment | added | Wolfgang Bangerth | It's almost always a good idea to refer to Hairer & Wanner :-) | |
| Nov 18, 2020 at 23:23 | comment | added | Chris Rackauckas |
This method is somewhat unstable though. It's really derived for explicit methods. In DifferentialEquations.jl, we still use this anyways, but with a failure case that if it asks for something too small then you just use 1e-6. And FWIW, Fortran radau's default is to always start 1e-6.
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| Nov 18, 2020 at 20:40 | history | edited | Laurent90 | CC BY-SA 4.0 |
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| Nov 18, 2020 at 20:33 | history | edited | Laurent90 | CC BY-SA 4.0 |
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| Nov 18, 2020 at 20:28 | history | edited | Laurent90 | CC BY-SA 4.0 |
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| Nov 18, 2020 at 20:23 | history | edited | Laurent90 | CC BY-SA 4.0 |
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| Nov 18, 2020 at 20:08 | history | edited | Laurent90 | CC BY-SA 4.0 |
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| Nov 18, 2020 at 20:02 | history | answered | Laurent90 | CC BY-SA 4.0 |