Timeline for Calculating the error in the solution of a system of ODEs
Current License: CC BY-SA 3.0
13 events
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| Oct 3 at 2:25 | comment | added | lotus2019 |
Hi, this line encountered an error after execution. With[{step = 100}, Plot[residuals /. s // Evaluate, Evaluate@Flatten[{t, (x["Grid"] /. s)[[{step, step + 1}]]}], PlotStyle -> Opacity[0.75], Frame -> True]] @Michael E2
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| Jun 16, 2020 at 9:23 | history | edited | CommunityBot |
Commonmark migration
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| Oct 19, 2016 at 13:00 | comment | added | Michael E2 |
@MMM It replaces all instances of Equal with Subtract. So if you have a == b, which is the typeset form of Equal[a, b], it becomes Subtract[a, b], which evaluates to a - b. In short, it gives the difference between the left-hand and right-hand sides of each equation in ode. Some people prefer Subtract @@@ ode, which replaces the head of each element in ode with Subtract; if ode is a list of equations as in this case, it has the same effect.
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| Oct 19, 2016 at 12:46 | comment | added | zhk |
@MichaelE2 Can you please explain this part of code residuals = ode /. Equal -> Subtract?
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| Oct 19, 2016 at 2:35 | comment | added | zhk | @MichaelE2 Thanks for such a detailed and wonderful answer. | |
| Jul 31, 2016 at 9:41 | comment | added | J. M.'s missing motivation♦ | @Michael, that's up to you; the reason why I brought those up is that I've found that it often surprises people that Bulirsch-Stoer is often able to take very long steps, until I gently remind that those long steps were created from extrapolating over a sequence of increasingly finer steps. (And after all, Bulirsch-Stoer is effectively equivalent to an RK method of very high order.) | |
| Jul 31, 2016 at 3:51 | comment | added | sara | @MichaelE2. This detailed explanation helped me a lot for calculating the error and as you have also given the error comparison obtained from three different methods. So now I solved my problem with ExplicitRK method which greatly reduces the error. | |
| Jul 31, 2016 at 1:32 | vote | accept | sara | ||
| Jul 31, 2016 at 1:32 | vote | accept | sara | ||
| Jul 31, 2016 at 1:32 | |||||
| Jul 30, 2016 at 22:04 | comment | added | Michael E2 |
@J.M. They produce (identical) solutions with fewer steps (31) than sRK (37) and residuals that are between those of s and sRK. The dense output is stored as piecewise Chebyshev series. (Should it be included? I thought it was getting overwhelming. Drat, just noticed another typo....)
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| Jul 30, 2016 at 21:45 | comment | added | J. M.'s missing motivation♦ |
It might be interesting to look at the InterpolatingFunction[] returned with either of the settings Method -> "Extrapolation" or Method -> "StiffnessSwitching".
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| Jul 30, 2016 at 21:41 | history | edited | Michael E2 | CC BY-SA 3.0 |
Fixed typos
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| Jul 30, 2016 at 19:01 | history | answered | Michael E2 | CC BY-SA 3.0 |
