MaplePrimes - answers and comments on Question, Export results

One way

Scott03 — Thu, 28 Jan 2010 21:29:54 Z

This isn't the only way you can do this but here is one way that should work. I have started with an example of the odeplot from the help page.

> with(plots);
> p := dsolve({y(0) = 1, (D(y))(x) = y(x)}, type = numeric, range = -5 .. 2);
> P1 := odeplot(p):

Now you have stored the odeplot in the variable P1. Now use the op command to take out the data from the plot structure.

> op([1, 1], P1);

Make sure that the above is an array in your case. If that is the case the following line will convert that Array to a Matrix and use the ExportMatrix command to export the data as a tab delimited file

> ExportMatrix("C:\\Test\\Mydata.txt", convert(op([1, 1], P1), Matrix), target = delimited, delimiter = "\t");

Scott
Application Developer
Maplesoft

Why odeplot?

Robert Israel — Thu, 28 Jan 2010 21:49:31 Z

Scott's method will work, but do you really need to use odeplot? dsolve(..., numeric) is the normal way to get the numerical solution of a differential equation or system, and with the output=<Array> option you get a Matrix containing the numerical values at specified points. In Scott's example, suppose you want the solution at all multiples of .001 from x=-5 to 2.

> X:= Array([seq(x, x = -5 .. 2, 0.001)]);
  S:= dsolve({y(0) = 1, (D(y))(x) = y(x)}, type = numeric, output=X);
  M:= S[2,1];
  ExportMatrix("C:\\Test\\Mydata.txt", M, target = delimited, delimiter="\t");

Thank You very much, Scott.

serilas — Mon, 01 Feb 2010 16:59:49 Z

Thank You very much, Scott. It seems to me that your one way is the best method for me. That’s just what I want. Thanks once more.

Robert thanks for help too. But your method isn’t for me. The point is that my system consists of 10 not easy differential equations. Now Maple computes it about hour (system will be complicate). In your case I must set step of computation. And that’s problem for me. I could be wrong but if I set short step the computation may slow down yet more. And if I set coarse step I run risks to withdraw the incorrect results. Whatever the case, odeplot function is optimized in this respect. It uses variable (optimal) step of computation for the space of all the working out process. Am I not right?

I still need help

serilas — Wed, 17 Mar 2010 13:09:47 Z

“With the default settings, I don't think odeplot gives you adaptive plotting: in my experiments, the interval between the t values plotted was constant.”

I don’t think so. You take a simple example. Try to increase the range of computation for a few orders and then you’ll see that step size isn’t constant in odeplot.
My task needs to compute system of ODE in the time span from 10^-22 to 10^-5. In the case when employs fixed step size I obtain too many unnecessary points (about 10¹⁷ points if I want to see result features in the total time range from 10^-22 to 10^-5). But odeplot function is convenient for me because it extracts points from full time range but these points are not many (minimal number of points is specify).
Now my system of equations consists of about 10 functions. Suggest me please, how export all the computation results obtained by means of odeplot function in a single text file? A structure of this file must be follow:

t                        F1                     F2                       F3
.1e-23                 2000.                   .1e-1                   0.
.630957e-21       2401.002702       .138391e-1       .411177e-2
.126191e-20       4801.010820       .435356e-1       .144869e-2
.789287e-20       7201.024351       .911873e-1       .810107e-1
.252382e-19       9601.043297       .139472e-2       .407977e-1
.832863e-19       12001.06765       .747403e-2       .160035e-1
.....                          .....                          .....                        .....

The first column corresponds independent variable (time), next columns correspond certain functions with titles for identification.

Searching of another way

serilas — Thu, 25 Mar 2010 12:21:54 Z

That doesn’t work in my case. Maybe I don’t know or understand something. I tried to do that in the following way (for example):

> restart; with(plots):
> sys:=diff(f1(t),t)=0.5/f2(t),
diff(f2(t),t)=sin(t),
diff(f3(t)*f4(t),t)=0.15,
diff(f3(t)/f4(t),t)=0.2*f2(t):
> init:= f1(0)=1, f2(0)=1, f3(0)=1, f4(0)=1:
> F:=dsolve({sys,init}, {f1(t), f2(t), f3(t), f4(t)}, numeric);
> W:=odeplot(F, [[t,f1(t)], [t,f2(t)], [t,f3(t)], [t,f4(t)]], 0..5.5):
> display(W);

Now all the calculated functions are located in W and I can plot them on the single diagram. But I don’t know haw export result from W into one text file in this case. Maybe who knows?

This way isn’t optimal

serilas — Sat, 27 Mar 2010 01:58:47 Z

In this case the system of ODE solving twice but time for me is very important. Expect about half hour once more don’t give more pleasure to me.