MaplePrimes - answers and comments on Question, How do I use the result of pdsolve(numeric)?

Suggestion

Markiyan Hirnyk — Sun, 13 Nov 2011 23:13:40 Z

Try
> U := subs(pds:-value(output = listprocedure), u(x, t));

[Length of output exceeds limit of 100000]
> U(3, 2);

0.183921336499484111
> A := Array([seq([seq(U((1/20)*j, (1/20)*k), j = 0 .. 20)], k = 0 .. 20)]);

Vector(4, {(1) = ` 1..21 x 1..21 `*Array, (2) =
`Data Type: `*anything, (3) = `Storage:
`*rectangular, (4) = `Order: `*Fortran_order})
> A(3, 11);
0.774910159896342488
A similar question was asked and answered here:
http://www.mapleprimes.com/questions/35619-Extracting-Numeric-Values-From-Pdsolve-Value
This link can be found by the "pdsolve,numeric" search in MaplePrimes at the top of this page.

PS. I obtain

> U(0, 0);

PPS. See pdsolve.mw

Plotting Array values

Robert Israel — Mon, 14 Nov 2011 05:41:06 Z

You can do a 3D plot of your solution directly with e.g.

> pds:-plot3d(t=0..1);

As for plotting an Array, you could do that with

> plots[surfdata](Array(A, datatype=float[8]), axes=box);

The datatype=float[8] option could have been included in the original definition of A, so it would be

> A := Array([seq([seq(U((1/20)*j, (1/20)*k), j = 0 .. 20)], k = 0 .. 20)],datatype=float[8]);
plots[surfdata](A, axes=box);

A just contains the values U(j/20, k/20) for j from 0 to 20 and k from 0 to 20, so A[1,1] = U(0,0). If you wanted U(-10, 0), you could have taken j from -20 to 20.

Export

Markiyan Hirnyk — Sun, 13 Nov 2011 23:54:14 Z

In order to export your data as text file you can do it in such somewhat modified way:
> A := array([seq([seq(U((1/20)*j, (1/20)*k), j = 0 .. 20)], k = 0 .. 20)]);

> A[3, 11];

0.774910159896342488

> writedata("c:/array.txt", A);
There are other ways to export data. Try the "export data" (or/and similar words) search in MaplePrimes.

Fourier analysis with Maple

Markiyan Hirnyk — Mon, 14 Nov 2011 00:49:31 Z

Maple has powerful tools for Fourier analysis. Look at ?fourier and this link .

Thank you for the answers, but, I am afraid,

Wavish — Mon, 14 Nov 2011 02:00:57 Z

Thank you for the answers, but, I am afraid, I am still struggling to understand Maple's philosophy. (My main analytical tool is IDL). I followed your suggestion, and got the array A. I check its dimensions by ArrayNumDims(A)and ArrayNumElems(A), it turned to be 2 and 441, respectively. I understand that 441=21*21, hence I have 21 points in both x and t directions.

But, when I print elements of the array, I am getting confused: print(A(1,1)) gives me 1. If these indices, (1,1), correspond to x=-10, t=0, the answer is not correct. Hence, I clearly don't understand what is in the array A. Also, when I am trying to plot it, plot3d(A,x=-10..10,t=0..4.5) I am getting "Error, (in plot3d) first argument must be either in standard or parametric form
". Hence, I am doing something wrong again... Also, having the array A, how can I make a plot of, e.g. A(*,0) - all possible values of x and t=0.

Sorry for silly questions! Thanks!

Aha, great. I did it. Now, U is a function,

Wavish — Mon, 14 Nov 2011 14:00:34 Z

Aha, great. I did it. Now, U is a function, and I can look at it's values at a certain (x,t) point:

> U(-1.3,0.2);

0.18889255096658836

But, when I am trying to make a plot of this function for a fixed value of, e.g., t, I am getting:

> plot(U(x,t=0.2),x=-5..5);

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

What am I doing wrong? I have also tried >plot(U(x,t),x=-5..5,t=0.2); with no effect.

Also, when I am looking at the value of an element of A, I am getting

> A[1,3];

0.960789439152323

which seems to be correct. But, can I make a 1D array with a certain line or column of the matrix A? If so, how should I plot it?

Thanks!