Stef Pillaert

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These are questions asked by Stef Pillaert

Hello,

Is it possible to solve a differential equation, where the solution is a 8x8 matrix u(t)?

The equation to solve for, "vgl", is this one:

The values for u(0) are known:

The functions QL(t) and RL(t) are also 8x8 matrix functions. They are actually Fourier series.

Can anyone point me in a direction how to tackle this in Maple?

For completness, I add the entire Maple worksheet (Toon.mw), but my last line obviously doesn't work ;-)

Also all the matrices for the Fourier series are added, just for completeness: RL0.txtRL1.txtRL_1.txtstrQL0.txtstrQL1.txtstrQL2.txtstrQL_1.txtstrQL_2.txtustart.txt

 

Any hints appreciated a lot!

Stef

Probably a dumb question, but I don't manage to read complex numbers from a text file, not even when the text file is created by Maple itself. I've been looking around, but didn't find an answer (which must be rather a simple one, I suppose).

Why is A not a matrix with complex numbers, as is B?

I have a lot (2000+) of irregular 3D data in an nx3-Matrix "M" (in the added example created via RandomMatrix, in reality actual experimental data), representing 3d coordinates. I manage to create a 3d plot of M via surfdata.

I also have a 3d-function "UC", I want to plot this function when it results into "1". I managed to plot this via implicitplot3d.

So far, so good, see the Maple file. (In reality, the UC function should be approximating the data in M, which obviously isn't the case here because of the randomisation :-)

But I actually want a 2D version of these plots:

  • with contour lines for equal values of the third column in M (the vertical axis) for the surfdata.
  • with contour lines for equal values of "n" in the UC function.
  • a combination of the two above in the same plot (M and UC together, as in the last 3D plot in my example, but in a 2d version). Of course, then there should be some way to make a distinction between the contour lines of M and UC (by using colours or appropriate symbols? Or one of the plots with clour bands, the other with contour lines?)

Is this at all possible? I've been trying by adding "dimension=2", "contour=10", ....: all efforts without succes....

Any help appreciated!

Stef


 

restart``

with(ExcelTools)``

with(LinearAlgebra); with(CurveFitting); with(Interpolation); with(plots); with(Statistics)NULL

``

NULL

M := RandomMatrix(200, 3, generator = 0 .. 1.00)

sdRES := surfdata(M); plots:-display(sdRES)

 

NULL

NULL

NULL

NULL

a := .45

.45

(1)

UC := proc (n, m__yy, m__zz) options operator, arrow; m__yy^2/min(1, (1-n)/(1+(-1)*.5*a))^2+(m__zz/`if`(n <= a, 1, 1-(n-a)^2/(1-a)^2))^max(1, 5*n) end proc

sdUC := implicitplot3d(UC(n, m__yy, m__zz) = 1, m__yy = 0 .. 1, m__zz = 0 .. 1, n = 0 .. 1, numpoints = 10000)

display(sdUC)

 

display({sdRES, sdUC})

 

NULL


 

Download test.mw

 

 

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