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These are replies submitted by student_md


The extension of Matlab files is ".m"

I wonder whether it is possible for Maple, too or not. It may be related to MS-Windows.


Thanks, Dear @Carl Love

I am clear in my third question.

#Let's define the followings

#We will define some functions in order to define the matrix psi
Tm:=(t,lambda,m)-> (2*(m-1+lambda)*t*Tm(t,lambda,m-1)-(m-1+2*lambda-1)*Tm(t,lambda,m-2))/m;  
L:=(m,lambda)->piecewise(lambda<>0,(Pi*2^(1-2*lambda)*GAMMA(m+2*lambda))/(m!*(m+lambda)*GAMMA(lambda)^2),lambda=0,2*Pi/m^2,lambda=0 and m=0,Pi);

#Now, we can define the matrix psi
psii:=(n,m,x)->piecewise((n-1)/2^(k-1) <= x and x <= n/2^(k-1), (2^((k)/2)/sqrt(L(m,lambda)))*Tm2(2^(k)*x-2*n+1,lambda,m), 0); 
psi:=(t)->Array([seq(seq(psii(n,m,t),n=0..M-1),m=1...2^(k-1))] ):

# A little edited version of Dear Carl Love's Code 
U:= Matrix(
            int(u(x,t)*psi(t)(j)*omega(iquo(j-1,M)+1,t), t= 0..1),
         x= 0..1


Thanks, @Carl Love,

Firstly; I added your code to my code in the question. But it doesn' t work.  So, I edited something. Can you check is it right, pls.?   

Secondly; I got the following result. u_11=0? or u_11=0.00001 etc.? 

Thirdly; you use omega[iquo(j-1,M)+1](t) instead of omega[n](t). But I think n=iquo(j-1-m,M)+1. Am I false?

@vv, Thanks for your interest.

I checked it, the function omega in the question is right.


Let function omega be any function that is greater than 0. What is your code for solving the question?


@Carl Love 

I think it is not a problem. But If you want, you can select lambda:=3/2 or lambda:=5/2 etc.

Thanks for your interest Dear @Carl Love,



  1. Yes, m goes from to M-1, not to M-1.
  2. No,  because there is also a function u(x,t) in the inner integral of original post. I edited it. 
  3. I edited the post and shared original screenshots from a book. The ns in the two integrals are not different. But I think it can be wrong. If they are ns, I can imagine our code. So, I agree with you. One corresponds to i and one corresponds to j.

 Meanwhile, I use Maple 2019.

Dear @Thomas Richard,

Thank you very much for your valuable contributions. Best regards.


Dear @tomleslie,

Yes, everything is OK now! :)


Many many thanks. I hope everything in your life happens as you desire.

@Kitonum result of the command pdetest is a 1x4 matrix [0,0,0,0] instead of 0. 

What do the elements of the zero matrix stand for?

The first element (first row, first column) of the matrix stands for ... ?

The second element (first row, second column) of the matrix stands for ... ?


@Rouben Rostamian  thanks for your interest.

I edited and expanded the question.  

@vv many thanks.

What is the purpose of using back quote 'if' ?

What is the difference from using just if?

Dear @tomleslie, you are right. The Maple numeric method is more accurate than my method.

What are the simple methods for finding maximum relative error, and max. absolute error at the interval?

Thanks, @vv

This is relative error, right?

How to find max. absolute error at the interval?

Dear @Carl Love, thanks for your feedback.

1- You are right, I corrected the post.

2- I removed local variable K.

3- Yes, it must be "*". I corrected it, too.

4- phii is not an external procedure. I corrected it as you say. (  phi[n, m+s-2*j](t) )

 I think the multiplication is commutative and also the matrix  is a symmetric matrix. 

Dear @tomleslie, thanks for your interest.

I think I am a misunderstanding. So, I edited the question.

After finding matrices by hand, we can write maple code for the matrices like you (Thanks again). But I want to find the matrices M,C,K etc. from the directly from the following equation by Maple.