Timeline for Why is NDSolve solving in term of two 1st order ODE slower than 2nd order?
Current License: CC BY-SA 3.0
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| Oct 15, 2012 at 18:43 | history | edited | fpghost | CC BY-SA 3.0 |
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| Oct 15, 2012 at 18:35 | comment | added | fpghost | I've added my working example (let me know if anything is missing; times I get for second order ~7s and ~21s for the first order reduction. I should note that my first order set is found by introducing a new dependent var $r^*$ related to the old $r$, and the $R:=r \Phi$ is the new independent var. These ICs are only good for $(\omega,\ell)=(1/10,1)$. The problem gets much much worse when $(\omega,\ell)$ get larger. | |
| Oct 15, 2012 at 18:32 | history | edited | fpghost | CC BY-SA 3.0 |
added example
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| Oct 15, 2012 at 15:13 | comment | added | Eric Brown | I'm interested in this, too. I thought Mathematica automatically decomposed the 2nd order ODE into a set of 1st order ODEs, and then those are solved. Maybe reducing the order by hand, taking into account certain simplifications that only you know, gives something faster than what Mathematica can deduce. On second read: Or maybe Mathematica finds a reduction that is better than what you have accomplished. | |
| Oct 15, 2012 at 13:12 | answer | added | Mark McClure | timeline score: 2 | |
| Oct 15, 2012 at 11:18 | comment | added | acl | an example would be helpful | |
| Oct 15, 2012 at 11:08 | history | asked | fpghost | CC BY-SA 3.0 |