How relevant are regularity, uniqueness and such “mathematical” concepts for engineering applications?
0
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How relevant are regularity, uniqueness and such "mathematical" concepts for engineering applications?
Possibly they're required for computation of the equations, no?
ordinary-differential-equations
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
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add a comment |
0
$begingroup$
How relevant are regularity, uniqueness and such "mathematical" concepts for engineering applications?
Possibly they're required for computation of the equations, no?
ordinary-differential-equations
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
$endgroup$
1
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
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Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
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– John Wayland Bales
Dec 24 '18 at 21:02
add a comment |
0
0
0
$begingroup$
How relevant are regularity, uniqueness and such "mathematical" concepts for engineering applications?
Possibly they're required for computation of the equations, no?
ordinary-differential-equations
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
$endgroup$
How relevant are regularity, uniqueness and such "mathematical" concepts for engineering applications?
Possibly they're required for computation of the equations, no?
ordinary-differential-equations
ordinary-differential-equations
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
asked Dec 24 '18 at 20:06
mavaviljmavavilj
2,80211037
2,80211037
1
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
$begingroup$
Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
$endgroup$
– John Wayland Bales
Dec 24 '18 at 21:02
add a comment |
1
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
$begingroup$
Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
$endgroup$
– John Wayland Bales
Dec 24 '18 at 21:02
1
1
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
$begingroup$
Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
$endgroup$
– John Wayland Bales
Dec 24 '18 at 21:02
$begingroup$
Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
$endgroup$
– John Wayland Bales
Dec 24 '18 at 21:02
add a comment |
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1
$begingroup$
Usually where the conditions for these theorems, like continuous right sides or a moderate, relatively global Lipschitz constant in the Lipschitz condition, are violated, you get in the numerical solution a stiff DE or something that has solutions stopping in the middle of the domain with no possible continuation.
$endgroup$
– LutzL
Dec 24 '18 at 20:20
$begingroup$
Just as an example, I once had a summer sabbatical with NASA engineers working on automatic docking in Earth orbit. I pointed out that there was no guarantee that a particular equation had a unique solution, and that, in fact it had two solutions. Luckily they were using the correct solution rather than the 'solution' which would have led to a collision.
$endgroup$
– John Wayland Bales
Dec 24 '18 at 21:02