John Starrett

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16 years, 211 days

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These are questions asked by John Starrett

I am trying to use fracdiff with a variable order argument, e.g. plot3d( fracdiff(x^2, x, t), x=0..1, t=0..2);

I get the error message "Error, (in fracdiff) Unable to determine ceiling of t"

but I am unable to find any information on this error.

 

I am fitting polynomial differential equations to data, and I came across some troubling behavior. I have sets of coordinates in x, y, z, and values w at these coordinates. The x,y,z coordinates and the data at these coordinates are concatenations of three subsets of data each, and depending on the order of the concatenation, I get different polynomials from the stats fit command. The difference is not trivial -- it makes a huge differentce in the stability of the differential equations. I have written a demonstration worksheet to show this problem.

John Starrett

Notice that the order of the output from the EulerLagrange command when three functions are input does not correspond to the order of the functions listed, and when they are requested separately, the last function is not included:

with(VariationalCalculus):

T3:=(1/2)*m*(diff(r(t),t)^2+r(t)^2*diff(theta(t),t)^2+diff(z(t),t)^2):
U3:=m*g*z(t):
L3:=T3-U3;

 


EL6:=EulerLagrange(L3,t,[r(t),theta(t),z(t)]);
EL6ra:=EulerLagrange(L3,t,r(t));

EL6thetaa:=EulerLagrange(L3,t,theta(t));
EL6za:=EulerLagrange(L3,t,z(t));


 



I have had this problem on all of my computers ever since Maple 11, I believe. No matter the number of points in a spacecurve or DEplot3d command, the graph comes out with gaps. For example, this is the output from Maple 14:




I have Maple 13.02 on an Acer Aspire 5532 (64 bit) and there are some severe problems with plotting curves using spacecurve, DEplot, or any plotting method that plots curves. When the option is set for anti-aliasing, I get curves like this: and when anti-aliasing is turned off, the curves look like this:
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