Timeline for Spectral Collocation (or Weighted Residual) Methods to solve Stiff ODEs?
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2015 at 19:00 | comment | added | jlperla | Sorry I triggered the comments on implicit Runge kutta methods with my suggestion of a possible connection. Your comments taught me a lot, though I agree they don't help answer the question. Thanks again | |
| Nov 8, 2015 at 10:12 | comment | added | David Ketcheson | The question is fine. My answer was mainly about clearing up misconceptions, which you have removed from the question. | |
| Nov 7, 2015 at 16:59 | comment | added | jlperla | The question is the same! I said that if an ODE is stiff (diagnosed through finite difference solutions, or whatever), then are projection methods such as collocation with a chebyshev basis appropriate to solve the ODE. You corrected me to change "projection methods such as chebyshev collocation" to "spectral methods such as spectral collocation with a chebyshev basis". But otherwise the question stands. This is a reasonable question as stiffness is a property of the ODE rather than of the solution method. | |
| Nov 7, 2015 at 10:24 | review | Close votes | |||
| Nov 8, 2015 at 10:18 | |||||
| Nov 7, 2015 at 10:05 | comment | added | David Ketcheson | This question has changed so much from what it originally was that most of my answer no longer makes any sense. In the future, I think it's better to ask a new question than to completely rewrite one that has already been answered. | |
| Nov 6, 2015 at 22:40 | history | edited | jlperla | CC BY-SA 3.0 |
edited body
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| Nov 6, 2015 at 18:13 | comment | added | jlperla | @DavidKetcheson You can now see the ODEs. Is this stiff? It has the hallmarks of a stiff system in solving it, BUT it is possible that what is causing those issues is actually the vanishing derivative term. I don't know... | |
| Nov 6, 2015 at 17:51 | history | edited | jlperla | CC BY-SA 3.0 |
Wrote out the ODEs.
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| Nov 6, 2015 at 17:15 | comment | added | jlperla | I copied that comment on stiffness from Wikipedia, but I am pretty sure I mean it in the normal sense of the term (even if I am communicating poorly). How do I know? Because it seems to have all the hallmarks of what people call a stiff system (e.g., when solving with finite differences the adaptive timesteps need to get incredibly small, etc.). The ODE is tricky and may not be a minimalist example, but I will post it for fun. | |
| Nov 6, 2015 at 12:11 | history | tweeted | twitter.com/StackSciComp/status/662603130509639680 | ||
| Nov 6, 2015 at 6:54 | comment | added | David Ketcheson | By "stiffness", you seem to be referring to something distinct from what I understand the term to mean. I can't really say more unless you write down your equations. | |
| Nov 6, 2015 at 0:20 | history | edited | jlperla | CC BY-SA 3.0 |
grammar and typos.
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| Nov 5, 2015 at 19:13 | comment | added | jlperla | Thanks, I would ask that for a separate question. But removing the implicit-Ruge-kutta comments from your answer (which I think I caused accidentally as they are not important for the question), I am not sure if the answer is clear for chebyshev spectral collocation. Are you sure that the same problems that stiffness causes in finite difference schemes wouldn't cause trouble with chebyshev methods I described? If so, I think that may be the answer. | |
| Nov 5, 2015 at 19:10 | comment | added | David Ketcheson | Regarding your new update: there are a positivity and monotonicity preserving methods you could use, but that is another topic. | |
| Nov 5, 2015 at 17:27 | history | edited | jlperla | CC BY-SA 3.0 |
Updated to use proper terminology of spectral methods.
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| Nov 5, 2015 at 17:21 | history | edited | jlperla | CC BY-SA 3.0 |
Updated to use proper terminology of spectral methods.
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| Nov 4, 2015 at 22:26 | history | edited | jlperla | CC BY-SA 3.0 |
added 27 characters in body; edited title
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| Nov 4, 2015 at 22:23 | comment | added | jlperla | The wikipedia article is saying exactly what I mean: "choose a finite-dimensional space of candidate solutions (usually, polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the given equation at the collocation points." | |
| Nov 4, 2015 at 19:35 | comment | added | David Ketcheson | By the way, "collocation" and "projection" refer to very many different things in the realm of numerical methods. In my view, what you are proposing is quite different from what is explained on the Wikipedia page you have linked to. | |
| Nov 4, 2015 at 19:32 | comment | added | David Ketcheson | I can't tell from what you have written whether you have an initial or boundary value problem. Since you refer to stiffness and Runge-Kutta methods, I would guess it is an initial value problem. But if so, this is a very expensive method since it couples all the time steps into one big system. | |
| Nov 4, 2015 at 16:58 | comment | added | jlperla | @DavidKetcheson See my edits. Thanks for looking at this! | |
| Nov 4, 2015 at 16:58 | history | edited | jlperla | CC BY-SA 3.0 |
Better description of projection methods.
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| Nov 4, 2015 at 7:15 | comment | added | David Ketcheson | Could you specify precisely what you mean by "projection methods", with equations or a reference? | |
| Nov 3, 2015 at 17:50 | history | asked | jlperla | CC BY-SA 3.0 |