@jahan The method that you use to solve the ODEs makes no difference. You say that you already know how to make a single plot. The command to combine multiple plots is plots:-display.

Please post your code as an attached worksheet. To attach a worksheet to a post, use the green uparrow tool that is the last item on the second row of the toolbar in the MaplePrimes editor.

@mangaba 

Using Windows 8 64 on an i7 with Maple 2015/64, I get the answer instantly.

Please attach the Standard (i.e., "Java") worksheet that you executed to get this error. Surely there is something suspicious about lend2-lend2, lenh1-lenh1, and degb1-degb1. Sometimes variables can be different even though they appear to be spelled the same, especially in 2D input. An expert can usually detect this by examing the worksheet.

The algebraic expressions in the first part of your Question are ambiguous. You need to use parentheses to clarify them. Also, your summation needs an upper limit. I guess n, but I'm not sure.

The second part of your Question, the part beginning "Also although", is a repeat of your Question from April 20. If you have a problem implementing the Answers that you got to that Question, then you should post a Reply in that thread.

@northpole11 

Here's a "sandbox" for testing/adjusting parameters:

pde1:= diff(f(x,t),t$2) - diff(f(x,t),x$2) = 0:
pde2:= subs(f= g, pde1):
sys:= {
     pde1
    ,pde2
};
INF:= 20:
IBC1:= {
     f(inf,t) = inf, f(x,0) = sin(x), f(-inf,t) = -inf
    ,g(inf,t) = inf, g(x,0) = sin(x), g(-inf,t) = -inf
    ,D[2](f)(x,0) = 0
    ,D[2](g)(x,0) = 0
}:
pds2:= pdsolve(sys, eval(IBC1, inf= INF), numeric, spacestep= .5):
pds2:-plot(f(x,t), x= -INF..INF, t= 0, numpoints= 100*INF);

It's set up to make commenting out specific lines easy. The maximum value of INF for which I get good results (that's with only looking at the t=0 plot) is 20. My guess is that the spacestep should be smaller than 1/4 of the period of the waves. For the initial conditions above, that would be Pi/2.

You wrote:

Anyway varying spacestep seems to help but i don't get the expected result with this.

Well, what are the expected results? I can't work on this without knowing.

What is the best way to set boundary conditions then?

Well, this is getting out of my area of knowledge, but I suppose that you mean What is the best value INF? The plot of the initial conditions gets "choppy" looking for INF >> 20, even at small values of spacestep and large values of numpoints.

@rbd66 

You may have already corrected these (as per your followup edit), but I thought that I'd mention anyway the two issues that I found. The first is that your restart command is in a text field rather than a command field. That's why it doesn't work. The second is that when you want to use the results of one command as input to a subsequent command, then you need to assign the results of the first command to a variable. You had

solve(..., {u[2,2], u[2,3]});
eval(< u[2,1], u[2,2], u[2,3] >, omega[2]);

That needs to be

omega[2]:= solve(..., {u[2,2], u[2,3]});
eval(< u[2,1], u[2,2], u[2,3] >, omega[2]);

or

results:= solve(..., {u[2,2], u[2,3]});
eval(< u[2,1], u[2,2], u[2,3] >, results);

or, for a quick-and-dirty computation,

solve(..., {u[2,2], u[2,3]});
eval(< u[2,1], u[2,2], u[2,3] >, %);

where the % represents the results of the most recently executed command, which is not necessarily the same as the command immediately above it.

Consider the first plot in this Post that's on a black background (it's simply a plot of a gold hemisphere). I guess that that plot was made in MapleSim. Is it possible to make that plot in Maple proper (minus the black background perhaps)? I want it exactly like that, with the metallic effect and the two lights.

This is the third time that you've posted this problem since March 7---only 1-1/2 months. Three of the top seven responders on this site have already given you input. Understand that no one here can help you further. It's not that this problem is uninteresting or that you've inadequately described it. I find it interesting. It's just too hard. Perhaps it's time to accept that this problem can only be solved numerically, not symbolically. There're a great many such problems. Do you have some reason to believe that this problem can be solved symbolically?

If you make progress on this problem, then post a followup to one of your previous threads. Don't make a new Question unless it's truly new. If you encounter any Maple-related issues in your investigations, then please do post them as new Questions. For example, your Question "D meaning in Maple" was a fine Question even though it involved this same problem.

Try posting in Stack Exchange's Math Overflow forum. That's their forum for research-level problems.

If I've misinterpretted your intent, and you actually do want to make a numerical comparison of these five functions, then ignore my comments above and please accept my apology: I was mistakenly inferring your intent based on your previous posts about this problem. There're numerous ways that we can use Maple to make a numerical comparison.

@c4meleon 

If you're truly sorry for what you did, then you will put back the original Question with the code that was in it, or some close approximation of that, and change the title to something appropriate. And if you're not sorry, then I'll never respond to your posts again.

And, no, I don't respect you, yet. But I could come quickly around to it if you come correct.

@testht06 

You wrote:

Of course I known R^4 = M and I checked by simply comnand Expand~(R^4) mod p;. But the problem is that if I excuted Your proc with M:= [ [x^2, x,1,1], [x^3,x^2+x,x^2+1,x^2+x],[x^3+x+1,x^3+x^2+x, x^3+x,x^2+x],[x,x,x^3+x^2+x+1, x^3+x+1], but not receive R= [[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,1,x,x^2].

But using the values for R and M that you give in the above paragraph R^4 is NOT equal to M!! That is clearly shown by the easy computation Expand~(R^4) mod p---a computation that doesn't involve my program at all. You say "Of course" and "I checked ... Expand~(R^4) mod p." Well, then attach a worksheet showing that you checked. Because if you're getting that R^4 = M, then there's a serious bug in Maple---a bug in basic matrix multiplication that's nearly beyond belief. I even did the matrix multiplication by hand, and I did not get M.

And with the following matrix

M:= < x^3+x^2+x, x+1, x^3+x+1, x^5+x+1; 
 x, x, 1, x+1; 
 x^3+x^2+1, 1, x^3+x+1, x^5+x^3; 
 x^4+x^3+x, x^2+x, x^4+x^2+1, x^6+x^2+x+1 >:

also not receive R=[[0,1,0,x],[1,0,1,0],[x,0,1,3],[1,0,1,x^2]], while R^3 = M

In this case it is indeed true that R^3 = M. But nth roots are of course not generally unique. In the cases that we've dealt with so far, the fourth roots of the eigenvalues were unique. That means that R was uniquely determined. In the case at hand, each eigenvalue has three distinct cube roots. That means that M has 3^4 = 81 different cube roots. Now, if you want, I could search through all 81 cube roots for those that can be represented in the original field. But that can be a lengthy search---which quickly grows much longer as ROOT and the order of the matrix increases.

Moreover, the input of this proc is any matrix, need to find R (R is completely unknown)

Uh-uh. First we work out all the bugs, kinks, and issues in the worksheet version. Then I'll make it into an actual proc procedure that will work for an arbitrary finite-field matrix M and positive integer ROOT.

@rbd66 

After or under makes no difference. Please post the worksheet showing it not working. Here's my copy of the worksheet showing the command working.

Earthquake_2_eval.mw

@Markiyan Hirnyk Yes, I forgot about the Explore command, and I agree with you.

DON'T EVER DELETE OR EDIT OUT THE BODY OF OR CHANGE THE TITLE OF YOUR ORIGINAL QUESTION AFTER IT HAS RESPONSES!!!! YOU HAVE JUST MADE THIS WHOLE THREAD WORTHLESS FOR OTHER/FUTURE READERS!!! IT'S NOT ALL ABOUT YOU AND YOUR QUESTION! HAVE SOME RESPECT FOR THE OTHER READERS AND FOR THE WRITERS WHO TOOK THE TIME TO RESPOND TO YOU.

Hello, and welcome to MaplePrimes.

1. Your boundary conditions use a parameter q which your post doesn't give the numeric value of. I can't debug this without that q.

2. I note that your f and g are not coupled; they can be solved separately. So my first step to debugging this would be to try to solve them separately.

3. pdsolve(..., numeric) is often very sensitive to its optional arguments spacestep, timestep, etc. I've often gotten results that were complete garbage (as you're getting) on the first try that could be corrected by adjusting the options.

4. What is the significance of your boundary positions -100 and 100? Are they stand-ins for infinity? If yes, then try making those -10 and 10 or -5 and 5. Get it working for those values first, and then, if need be, gradually spread them out.

5. In the future, please post your code as plaintext and/or as an attached worksheet. (Plaintext is the format that you used for the parameters r0 and theta0.) This is so that no-one has to retype it. To attach a worksheet, use the green uparrow tool, which is the last item on the second row of the toolbar in the MaplePrimes editor.