Timeline for Using leapfrog method to solve system of ODE's
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2023 at 15:51 | comment | added | VasiliBilly | That is very helpful, thanks alot for your help! | |
| Jun 6, 2023 at 15:57 | comment | added | Michael E2 | Right, as far as I know, separability is a requirement for symplectic methods like leapfrog. | |
| Jun 6, 2023 at 13:56 | comment | added | VasiliBilly | @MichaelE2 Does this mean that since my potential is non-seperable, I cannoit use this method? | |
| Jun 6, 2023 at 0:02 | history | edited | Michael E2 | CC BY-SA 4.0 |
Added message name
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| Jun 4, 2023 at 19:45 | comment | added | Michael E2 |
Further, to apply a symplectic method, not only does the vector field have to split, it has to be separable. But your system is not separable. For instance $(x',y',x'',y'')=F(x,y,x',y') = A(x,y)+B(x',y')$ with the $x'',y''$ components of 𝐴(𝑥,𝑦) being zero and the $x',y'$ components of $B(x',y')$ being zero. Here the qvars are {x, y} and the p variables are {x', y'}. (Note: I'm writing x' and y', but when the system is converted to first-order, I'd give them new variables, say xp for x' and yp for y' -- or whatever names you like).
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| Jun 4, 2023 at 19:45 | comment | added | Michael E2 | Note that for the method "Splitting", the documentation seems to imply the problem must be cast in a first-order autonomous form $u'=F(u)$, where $u$ would be the vector $(x,y,x',y')$ in this case. OTOH "Splitting" does not complain about second-order ODEs, which leaves open the possibility that it does handle higher-order equations. But I think not.... | |
| Jun 4, 2023 at 15:24 | comment | added | Michael E2 |
Syntax error: qvars = {x[t], y[t], x'[t], y'[t]};. It would also be nice if semicolons where at the ends of the parameter assignments. Their output is unnecessary.
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| Jun 4, 2023 at 15:15 | history | edited | VasiliBilly | CC BY-SA 4.0 |
added 426 characters in body
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| Jun 4, 2023 at 15:09 | comment | added | VasiliBilly | @I.M. trying it out this way still seems to not work, I have included the edited code | |
| Jun 2, 2023 at 16:35 | comment | added | I.M. |
From your link SymplecticLeapfrog = {"SymplecticPartitionedRungeKutta", "DifferenceOrder" -> 2, "PositionVariables" :> qvars};. Another options is NDSolvePlugIns
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| Jun 2, 2023 at 14:43 | comment | added | xzczd♦ | Related: mathematica.stackexchange.com/a/274544/1871 | |
| S Jun 2, 2023 at 14:20 | review | First questions | |||
| Jun 2, 2023 at 14:46 | |||||
| S Jun 2, 2023 at 14:20 | history | asked | VasiliBilly | CC BY-SA 4.0 |