Timeline for Backwards Difference Implicit Method for Nonlinear Parabolic PDE in Python
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 16, 2021 at 19:32 | comment | added | boyfarrell | Methods of lines might work well; you just need to worry about you spatial discretisation and leave the time stepping up to the solver. scholarpedia.org/article/Method_of_lines | |
| Jan 16, 2021 at 16:48 | comment | added | AlphaArgonian | My discretisation formula must be wrong then, I'll go back through it. Thanks for all of this. | |
| Jan 16, 2021 at 16:41 | comment | added | Lutz Lehmann | C-N is, on the m-o-l level of abstraction, nothing more than the implicit trapezoidal method. I added the equations and code for it. | |
| Jan 16, 2021 at 16:40 | history | edited | Lutz Lehmann | CC BY-SA 4.0 |
add implementation of Crank-Nicolson
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| Jan 16, 2021 at 16:18 | comment | added | AlphaArgonian | I've tried modifying this for the Crank-Nicolson scheme and I get a broadcast error for the ``` dU[1:-1] ``` stage. | |
| Jan 16, 2021 at 15:53 | history | edited | Lutz Lehmann | CC BY-SA 4.0 |
derivative of boundary condition
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| Jan 16, 2021 at 15:22 | history | edited | Lutz Lehmann | CC BY-SA 4.0 |
odeint, section headers
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| Jan 16, 2021 at 13:55 | comment | added | Lutz Lehmann | You could of course use any explicit ODE solver method. The problem is that the dissipation term is smoothness-reducing, using the inversion in implicit solvers reverts that to a smoothness-enhancing behavior. Then there is operator-splitting where you only solve the linear dissipation term with an implicit method or matrix exponential and the non-linear term with an explicit method. But since that leaves derivations on the explicit side, this might not be overarchingly effective. | |
| Jan 16, 2021 at 13:50 | comment | added | Lutz Lehmann | You have a system of cubic equations in the new vector. There is no (sensible) way around the iterative numerical solution. If you call that Newton's method (with a sensible initial guess) or predictor-corrector scheme does not make a difference. Using BDF or Adam-Bashford formulas or similar you can get a higher order predictor, perhaps reducing the number of necessary corrector iterations. // One can solve polynomial systems algebraically, with horrendous time and space complexities, this is certainly not a short-cut. | |
| Jan 16, 2021 at 13:45 | comment | added | AlphaArgonian | Wow I never thought to do it like this, thanks! Do you know how you could do it without using a predictor-corrector method? | |
| Jan 16, 2021 at 0:47 | vote | accept | AlphaArgonian | ||
| Jan 15, 2021 at 23:10 | history | edited | Lutz Lehmann | CC BY-SA 4.0 |
use explicit LU decomposition
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| Jan 15, 2021 at 22:57 | history | answered | Lutz Lehmann | CC BY-SA 4.0 |