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.

restart: #Let's define the followings k:=1: M:=2: f:=x*t: N:=2^(k-1)*M: lambda:=1: u:=unapply(f,x,t); omega:=(n,x)->(1-(2^k*x-2*n+1)^2)^(lambda-0.5); #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; Tm(t,lambda,0):=1: Tm(t,lambda,1):=2*lambda*t: Tm2:=(tt,lambda,m)->subs(t=tt,Tm(t,lambda,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( N, (i,j)-> int( psi(x)(i)*omega(iquo(i-1,M)+1,x)* 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.? edited_answer.mw

**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?**

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,

**Yes, m**goes from**0**to**M-1**, not**1**to**M-1**.**No, because there is also a function u(x,t) in the inner integral of original post. I edited it.**- I edited the post and shared original screenshots from a book. The
**n**s in the two integrals are not different. But I think it can be wrong. If they are**n**s, 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 @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 ... ?

etc.

@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?

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.