should this be Pgamma2

@nm 

There can be many reasons why a graphic card is part of an issue. For example, the system is configured not to use the graphic card and used the internal graphic adpter.

You can check this in the task manager under GPU. With the NVDIA control center you can force which adapter is used by javaw.exe.

A driver update could make sense.

I am on Windows 10.

@nm 

no hang when printing but when expanding. The thread 0x000000000000, to what I have observed so far, signals a dead end. 

And no black window. You should have an NVIDIA control pannel. You could check under 3d settings which graphic processor is used. My system is set to automatic.

Allocated memeory was also moderate.

Strange.

That was with

The superposition of two linear polarized orthogonal waves can create circular polarization provided that there is an appropriate phase shift beween the waves.
The compound field vector is often animated as a rotating vector where the tip is describing a helical path.

What I like about your way of generating the helix is the use of sectioning of two surfaces. It's the first time I see it this way. The compact and clean coding is nice as well.

@nm 

Could you provide a test file? What I see in your video is extreme. I only have these black or clipped windows when I have a Maple session running for a long time with many worksheets open. The clipping is also visible in other applications running in parallel which is an indication that the memory for the graphics adapter (virtual or phsyical?) is running out.

After a logout from Windows everything is back to normal.

Anything special about your graphic adapters?

Yes, I had this before. It happens from time to time and I assume it is related to Java and Windows.

If Crtl,Shift,Enter still executes the worksheet then something hinders the GUI to enable the !!! button.

You could also try to change worksheet tabs to see if that enables the button. This "method" enabled in some instances the interupt button.

@ecterrab 

I have done a punctual check of the new solutions provided by dAlembert. Looks good, but provides less solutions in the real domain.
For me it is not a first choice to solve this initial value problem. odeadvisor still does not list this type. Is it for the reason that other methods are considered superior? Anyway, IVPs leads me to a subtely that I overlooked when speculating about odeadvisor.

odeadvisor advises on ordinary differential equations and not on initial value problems. In this sense, no suggestions on methods are made to solve an IVP. 👍

@dharr 

I have tried on the solution obtained with the dsolve method dAlembert

subs(x=-4,sol);
allvalues(%,implicit = true);

Only one root is obtained for negative x whereas 3 roots are obtained for x beeing positive. To make sure I also set one of the roots not obtained with dAlembert as root selector

RootOf(op(rhs(sol)),-4.725448724):
allvalues(subs(x=-4,%));
evalf(%);

-> -4.721 is not a root.

Looks to me that the RootOf expression obtained with dAlembert is not pointwise equivalent to your implicit solution. It provides less solutions to the ode. All that assuming that RootOf performs as described on the allvalue helppage  (i.e. it provides all roots).

Again 👍👍

@dharr 

Its apparent from your solution that allvalues did not provide all solutions when working symbolically and did also not warn about missing solutions when working numerically. Why allvalues decided to solve numerically in one case is still unclear.

Implicitly your answer sheds light on questions about the results of dsolve depending on solution methods. That is very revealing.

Thanks allot!

Have you forgotten to add an attachement?

@

Very interesting background.

I wonder to what extent such advanced integration methods will one day be available in Maple's standard libraries. Perhaps the need for more PDE functionality and/or performance will trigger this. Some users have asked for it.

Thank you!

@nm 

Or nothing at all, as here if the rhs is <>0

duffing:=m*diff(y(t),t,t) + b*diff(y(t),t) + c1*y(t) + c3*y(t)^3  =  F(t);
DETools[odeadvisor](duffing,y(t));
             /  2      \                                          
             | d       |     / d      \                    3      
duffing := m |---- y(t)| + b |--- y(t)| + c1 y(t) + c3 y(t)  = F(t
             |   2     |     \ dt     /                           
             \ dt      /                                          

  )


                             [NONE]

What irritates me more is the implicit solution, which seems to pass odetest only if the singular solution is taken into account

DETools[dalembertsol](ode):
solve(subs(x=0,y(0)=0,%[1]),{c__1});
sol3:=subs(%,%%[1]);
simplify(odetest(sol3,ode));
subs(sol,%);

Not sure how to interprete this. Is, in this case, this solution for this IVP a valid solution? Can provide dAlembert a solution at all or is it for that reason excluded from the list of methods? This would mean that certain pattern of methods are not possible.

@nm 
This pattern should also give a true. Shouldn't it?

`odeadv/y=_G(x,y')`

@nm

Maple agrees too

DEtools:-odeadvisor(ode,[dAlembert])
                          [_dAlembert]

However, it looks to me that the method [_dAlbembert] does nothing more than this call to DETools (to be confirmed)

DETools[dalembertsol](ode);
solve(subs(x=0,y(0)=0,%[1]),{c__1});
subs(%,%%[1]);
plots:-implicitplot(%)

which does not accept ICs but returns 2 solutions where one of them comes with an integration constant.

No IC are accepted here

DETools[dalembertsol](ode,ic);
Error, (in ODEtools/info) found wrong extra argument(s): y(0) = 0

A call of dsolve with the method [_dAlbembert] should probably do the same or return the implicit solution from above.

We could also ask, why Maple did not list the type dAlembert. Maybe it is done on purpose to suggest/advise most suitable methods.

@Carl Love 

Thank you. The links are helpful. What was not helpful in the context of this question was how I got introduced to the term homogeneous a long time ago.

Maple does not seem to classify the "other" homogeneous cases that Wikipedia mentions in the link above as such and uses different terms. I am referring here to

Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.