Timeline for Variation of heat equation with guessed initial condition
Current License: CC BY-SA 4.0
24 events
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| Jun 25, 2022 at 11:50 | history | edited | xzczd♦ | CC BY-SA 4.0 |
Add notes about bug of ComplexExpand. Simplify the code with diffbc.
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| Feb 1, 2019 at 15:34 | history | edited | xzczd♦ | CC BY-SA 4.0 |
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| Feb 1, 2019 at 15:02 | history | edited | xzczd♦ | CC BY-SA 4.0 |
Simplify the code further
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| Feb 1, 2019 at 14:48 | history | edited | xzczd♦ | CC BY-SA 4.0 |
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| Oct 23, 2018 at 7:47 | history | edited | xzczd♦ | CC BY-SA 4.0 |
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| Jan 21, 2018 at 23:16 | comment | added | Boson Bear | Thanks for pointing me to it! Actually, I was thinking about acknowledging your contribution in the acknowledgement section of my paper, adding citation, or even future collaboration on a few physics motivated numerical problems. I guess that involves too much personal info so I totally understand if you prefer to being anonymous. Otherwise, drop me a line at [email protected] if you would like to chat a lil bit. Also, I have a somehow related question here. Any comment is welcome | |
| Jan 21, 2018 at 17:19 | comment | added | xzczd♦ | @BosonBear There already exist discussions about this topic in meta :) : mathematica.meta.stackexchange.com/q/968/1871 mathematica.meta.stackexchange.com/q/1195/1871 | |
| Jan 21, 2018 at 15:28 | comment | added | Boson Bear | Thanks a lot. I'm working on a project where solving this efficiently is part of it. Since you've helped me a lot in the past a few days, I wonder if there's any way to acknowledge it properly in my paper if the work comes to fruition. Cheers! | |
| Jan 20, 2018 at 8:12 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 20, 2018 at 8:01 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 19, 2018 at 15:50 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 19, 2018 at 15:23 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 19, 2018 at 15:03 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 19, 2018 at 14:50 | comment | added | xzczd♦ |
@BosonBear Increasing the spatial grid points (in this case points) is almost the only way, as far as I know, but then the previous approach turns out to be slow. I've edited the post the include a more efficient approach, check the edit. BTW, a quick test shows, difforder=2 seems to be accurate enough for the system and make the calculation faster.
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| Jan 19, 2018 at 14:47 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 19, 2018 at 14:06 | vote | accept | Boson Bear | ||
| Jan 19, 2018 at 13:57 | comment | added | Boson Bear |
I see. So when I plot it out at a slice of r with respect to t, the plot is a bit zig-zag due to numerical noise. I wonder what the most efficient way is in order to increase the precision in the t direction?
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| Jan 18, 2018 at 16:54 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 18, 2018 at 16:34 | comment | added | xzczd♦ |
@BosonBear To be precise, it's for making Mathematica use an ODE solver rather than a DAE solver for solving the discretized system. If we don't differential the 2nd equation, after discretization the 2nd equation will become a set of algebraic equations that doesn't involve derivative of t, so NDSolve will choose a DAE solver for solving it, which doesn't work well on this problem. (You'll see icfail then. ) BTW the seemingly strange definition of odebc is also for adding derivative of t to the boundary condition.
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| Jan 18, 2018 at 16:00 | comment | added | Boson Bear | Thank you much for the detailed explanation. This is very helpful! Actually I did notice that simply adding a time derivative term could solve the system although it altered the equation. Am I right to think that you added a total derivative on both sides of the second equation just to tell Mathematica to choose the right PDE solver? | |
| Jan 18, 2018 at 8:21 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 18, 2018 at 8:10 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 18, 2018 at 8:04 | history | edited | xzczd♦ | CC BY-SA 3.0 |
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| Jan 18, 2018 at 7:09 | history | answered | xzczd♦ | CC BY-SA 3.0 |