DE - help

Muzialis-disabl · ‎Jun 17, 2009

Hi All,

I preface I apologize for how trivial this post might look, but unbelievably the HELP in my Mathcad is crushing the software I am unable to open it.

I am trying to solve the DE

d/dx (a*sin(x)*du(x)/dx)=0

Odesolve, which I remember by heart, is not apparently doing the job.
I remember a runge - Kutta solver is available but that is all I know, any help would be very appreciated.

thank you

Muzialis

ptc-1368288 · ‎Jun 17, 2009

Read the chapter "Derivative under Integration". Your setup does not make sense. Try something to get something.

jmG

Muzialis-disabl · ‎Jun 17, 2009

jmG,

thank you very timefor your reply and the time taken to do so, in spite of your appalling manners.

I am not sure I understand what can be possibly wrong with my setup.
It seems a very conventional DE to me.
Using some basic calculus, I could also have expressed it more explicilty, but I am not sure why I should have.

Maybe the boundary conditions? Would it be better if the both referred to the left most point of the intergration interval?

Thank you again

Muzialis

ptc-1368288 · ‎Jun 17, 2009

>I am not sure I understand what can be possibly wrong with my setup.<<br> __________________________

You just don't have a DE, the error message confirms. You may have wrongly interpreted the book style of the document you are reading.

jmG

Muzialis-disabl · ‎Jun 17, 2009

JmG,

I have to apologize for my insistence, but I am struggling to understand how could that not be a DE.

Is this one then, obtained by developing the original expression, a DE ?

cos(x)*u'(x)+sin(x)*u''(x)=0

I wish I was reading a book, at least I could scan a copy for you to explain me how to interpret the symbols.

If it could clarify the issue and resolve the misunderstanding, the equation simply expresses in 1 - D the continutiy of the stress in a beam with oscillating modulus.

u (x) = displacement
u' (x)= strain
sin ( x) = modulus
sin(x) * u'(x) = stress

whose derivative has to be zero due to equilibrium.

Thank you for your time

Best Regards

Muzialis

mzeftel · ‎Jun 17, 2009

If you have Mathcad 14, you can download the E-book, Inside Mathcad: ODEs and DAEs in Mathcad from the Mathcad Resource Center on www.ptc.com.

Mona

ptc-1368288 · ‎Jun 17, 2009

>Is this one then, obtained by developing the original expression, a DE ?

cos(x)*u'(x)+sin(x)*u''(x)=0<<br>

u''(x)*sin(x)*+u'(x)*cos(x)+"a relation with the primitive"=0

It would be less confusing if you would respect the traditional Mathcad setup. Yes that one could be by completing the missing term. Otherwise it's a kind of boundary DE.

jmG

Muzialis-disabl · ‎Jun 17, 2009

jmG,

I really do not understand what the term you are referring to is, actually why it is needed at all, but nevermind.

Your sheets reports example of constant coefficients DE, which is fine but not that relevant.

I was hoping that the misunderstanding was due to my very bad choice of the function depicting the modulus. The DE lost its physical significance and become quite badly posed as is depicting a material with locally a negative modulus, which is unrealistic.

Maybe I am missing something but nevermind,we will find a way.

Still thanks for your help and time.
Of course, if anybody else had anything to add I would be pleased to read about it.

Best Regards

Muzialis

ptc-1368288 · ‎Jun 17, 2009

>Maybe I am missing something ...<<br> _____________________________

Yes, a DE "equates" therefore solving a DE is solving for the function, whether symbolic or numerical. Here you just have the definition of a composite integrand of which one member is whatever you want or have. Solving this integral = 0 solves for the point of tangency horizontal , but you can solve for any slope in the � system.
So, you don't have a DE, just a two components ID [Integrand Definition], then solving for the integral at the given ID = 0 or else user slope.

Obviously, g(x) is something that belongs to your project, that can only be "demo" to validate the general interpretation attached.

jmG

ptc-1368288 · ‎Jun 17, 2009

... on your other point: "variable coefficients", there are no variable coefficients because there is no DE. Hope it demystifies your visit ?

jmG

Fred_Kohlhepp · ‎Jun 19, 2009

On 6/17/2009 10:31:24 AM, Muzialis wrote:
>JmG,
>
>I have to apologize for my
>insistence, but I am
>struggling to understand how
>could that not be a DE.
>
>Is this one then, obtained by
>developing the original
>expression, a DE ?
>
>cos(x)*u'(x)+sin(x)*u''(x)=0
>
>I wish I was reading a book,
>at least I could scan a copy
>for you to explain me how to
>interpret the symbols.
>
>If it could clarify the issue
>and resolve the
>misunderstanding, the equation
>simply expresses in 1 - D the
>continutiy of the stress in a
>beam with oscillating modulus.
>
>u (x) = displacement
>u' (x)= strain
>sin ( x) = modulus
>sin(x) * u'(x) = stress
>

In what context is modulus a function of position? Your equation has cos(x)*u'(x). If that's stress then sin(x)*u''(x) must also be stress; what does that make sin(x)?

Fred Kohlhepp
fkohlhepp@sikorsky.com

GuyB · ‎Jun 17, 2009

On 6/17/2009 5:44:44 AM, Muzialis wrote:
>...
>I am trying to solve the DE
>
>d/dx (a*sin(x)*du(x)/dx)=0
>
>Odesolve, which I remember by
>heart, is not apparently doing
>the job.

Odesolve has it's share of problems, but in this case it wouldn't help even if it worked. The biggest problem is your choice of ODE: the solution isn't defined at one of your endpoints, and blows up between it and your other endpoint.

- Guy

TomGutman · ‎Jun 17, 2009

What version of Mathcad? They are all different.

What is your problem with the help? You really need to straighten that out if you expect to be able to use Mathcad effectively. Have you tried a repair install? A reinstall?

Your equation, as given, is not suitable for ODESolve as you have a derivative of something other than the unkown function. You can use the symbolic processor to expand it into something which is useful. But the boundary conditions don't work. Whether they are simply impossible of just not findable by ODESolve I don't know.

ODESolve is just a wrapper around one of the command line solvers (you get a bit of a choice, including the tow R-K integrators). You can do the setup yourself easily enough (see my sheet on stiff ODE setup). But you have to solve the boundary value problem yourself, the command line solvers work only with initial values.
__________________
� � � � Tom Gutman

Muzialis-disabl · ‎Jun 18, 2009

Guy and Tom,

thank you very muhc for your valuable hints.
Guy points out very clearly what the problem is with the DE, which is related as I said to my really bad choice of the coefficient sin(x) which makes a solution unfeasible.
I have reinstalled MathCAD, everything is fine and the DE, with the substituion for example sin(x)+2 instead of sin(x), is solved brllinatly by Odesolve.

I still would have liked to understand what jmG was about, but you have to feel content with what you have do not you?

Thanks again to all

Muzialis

TomGutman · ‎Jun 18, 2009

>>I still would have liked to understand what jmG was about<<

I have long given up trying to understand jmG, or to educate him. He has explained himself very clearly in http://collab.mathsoft.com/read?124709,7 . I don't dare quote it, having gotten in trouble for saying much less.
__________________
� � � � Tom Gutman

ptc-1368288 · ‎Jun 18, 2009

>I still would have liked to understand what jmG was about<<br> __________________________

I have explained why you don't have a solution , because you don't have a DE, because you can't equate components or terms. Conclusively you can't "isolate the highest derivative" [Mathcad is telling you that in the error message]. If you don't trust what Mathcad, Mathematica are saying ... same in different words, then try Maple or else CAS solving DE's.

A DE represents the infinitesimal components of a system. For it to be solvable by symbolic or numerical solvers, components must "equate". It then implies the highest order derivative must exist. In your representation, it does not exist by inspection , Mathcad error message confirms. The Mathematica error message tells differently "input is not an ordinary differential equation".

Your representation is either incomplete or incorrect. If you figure you have something and wish to be checked, post it. I'm not saying your project is not solvable, NO ! Simply that some steps are missing to arrive at a solvable DE or that your representation needs be transformed or completed.

If it does not help, just discard.
Mathematica solves example 2, Mathcad does NOT.
Can you trust what Mathematica is telling about your input ?

jmG

PhilipOakley · ‎Jun 18, 2009

I think some of the the help is written in the "If I were you I wouldn't start from here" tone!

The help file could be more helpful, perhaps with an example (e.g. yours 😉 that shows when the message might occur and what you would change to make it right...

Philip Oakley

Muzialis-disabl · ‎Jun 18, 2009

jmG,

I am replying because of gratitude for all the help provided to me in the past.

But I am afraid on this one the quality of your posts is not as high as usual.

I understand decently well the difference between an algebraic expression and a DE.

The problem here seemed to lie

1) in the notation, as Mathcad requires the derivatives to be explicited (but this does not mean the original expression is not a DE)
2) in the bad choice of the example which made the problem ill

All the rest, I fear, I can not understand, which is evidently nobody's but mine problem.
I do not believe in full honesty though that anybody could claim that

d/dx (f(x)*du(x)/dx)=0

is not a DE.
I am not looking for sterile discussions here, my problem thanks to all of you is solved and I am off to the oub.

Have a good evening all of you

Marco

ptc-1368288 · ‎Jun 18, 2009

Marco,

if d/dx (f(x)*du(x)/dx)=0 would be a DE, both Mathcad and Mathematica would solve. Both issue the same message in short "Not a DE" then Not a DE. Plug f(x), plug u(x) and Mathcad has no problem to solve for the x at which point you prescribe the slope to be.

So, there are 4 idiots in there: Mathcad, Mathematica, jmG, and Tom Gutman who can't educate me ! Can you find more idiots trying Maple, Matlab ... etc. If yourself or your colleagues have worked out or completed or else transformed the base expression, pass it for the community, as a plotted function or as a data set to fit. Not anything that has d/dx is a DE.

jmG

TomGutman · ‎Jun 18, 2009

>>if d/dx (f(x)*du(x)/dx)=0 would be a DE, both Mathcad and Mathematica would solve.<<

Not true.

It is a DE. But it is not in the form that Mathcad's ODESolve can handle. There are very specific rules for the forms that ODESolve can handle (which differ somewhat from version to version).

As to Mathematica, it might well be able to solve it if it were properly written. Even without knowing Mathematica it is clear that your input to Mathematica does not represent the given DE.
__________________
� � � � Tom Gutman

Muzialis-disabl · ‎Jun 19, 2009

Hi All,

just to wrap this thread up I attach a sheet with the DE solved, after a modification in the origianl expression to make it well posed.

Thank you

All the Best

Muzialis

ptc-1368288 · ‎Jun 19, 2009

On 6/19/2009 6:17:52 AM, Muzialis wrote:
>Hi All,
>
>just to wrap this thread up I
>attach a sheet with the DE
>solved, after a modification
>in the original expression to
>make it well posed.
>
>
>Thank you
>
>All the Best
>
>Muzialis
______________________________

Not so well posed unless for this very unknown particular case, my point here is your particular case a > 1. "The original expression, modified to avoid singularities",
YES ! but that is ! insufficient!
You must pursue the general case

jmG