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I wonder which one is more accurate when solving differential equations?

- Mathematica
- Thread starter ENDLESSYOU
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- #1

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I wonder which one is more accurate when solving differential equations?

- #2

mfb

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Smaller numerical errors? Depends on the way you try to solve it, internal details of the programs and the accurary you need.

Less bugs? No idea

- #3

jim mcnamara

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Generally, software that is inaccurate or does calculations incorrectly either gets corrected by its authors or people stop using it. And users find something that does work as intended.

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Hmm. I would have thought ode45 would be a better choice for that problem in most cases. It's the one Mathworks use in their documentation - http://www.mathworks.co.uk/help/matlab/math/ordinary-differential-equations.html?s_tid=doc_12b

What led you to ask the question? Do you see any significant differences between Mathematica and Matlab? It doesn't address your particular case, but several years ago I partially-validated Matlab 6-dof simulation in Mathcad - the two applications gave very good agreement using a fixed 4th-order RK.

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They're stiff differential equations so ode15s might be a better choice. In my experience, MATLAB is more 'stable' than Mathematica. I once executed a same nb file on Windows and Ubuntu, but I got two different results.Hmm. I would have thought ode45 would be a better choice for that problem in most cases. It's the one Mathworks use in their documentation - http://www.mathworks.co.uk/help/matlab/math/ordinary-differential-equations.html?s_tid=doc_12b

What led you to ask the question? Do you see any significant differences between Mathematica and Matlab? It doesn't address your particular case, but several years ago I partially-validated Matlab 6-dof simulation in Mathcad - the two applications gave very good agreement using a fixed 4th-order RK.

- #8

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Are running modified DEs or getting very close to the "mass" centres? IME, the 3-body problem isn't generally treated as still, and the adaptive rk45 solver is usually good enough. Have you compared the results of running ode15 vs ode45?They're stiff differential equations so ode15s might be a better choice.

OK, that would make the Mathematica implementation a bit more suspect. Are there global parameters in the 2 versions of Mathematica that might be different? How does the Mathematica version compare to the Matlab in the same environment?In my experience, MATLAB is more 'stable' than Mathematica. I once executed a same nb file on Windows and Ubuntu, but I got two different results.

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