@nk2016   You do not have to type anything. Just copy it as text into the window of your worksheet and press the "Enter" key.

@Zeineb   if  F=1

@spalinowy  Why copy manually? In the file the simplified system has the name  Sys, and it can be used for further work with the system using the desired packages.

@spalinowy   I removed all called packages, including MTM, made restart at the beginning of the worksheet. Now it works.

Model_Maple3.mw

@spalinowy  Put here your system, or the link to the worksheet.

Should be  

MTM:-solve(5*x-3 = 19);

@vv   Very witty and beautiful solution, vote up! 

It's a pity that the symmetry is broken for any even N.

@vv  Problem point is that each line should intersect with each line. Only in this way we get the maximum number of pieces. I do not know whether there is such a turn-symmetric structure if  n>5

@Mac Dude  Of course this is not the completed code, but only the beginning. OP wants to solve the original partial differential equation by difference method and, therefore, replaces each derivative by the corresponding difference quotient.

@jga  It may be helpful for you that your function can be decomposed into partial fractions:

f:=1/(1+q)^4/(1-q^2)^2*q^4*(q^2+1)*(((q^6+q^5-q^4-2*q^3+q+1)^6/q^13+(q^6+q^5-2*q^3-q^2+q+1)^6/q^25)):
convert(f, parfrac);

@mehdibaghaee  To better understand what you have got, execute at the end  a few commands, for example

A;
A(1, 1);
A(1, 1)[1, 1, 1];
A(1, 1)[2, 2, 5];

@mehdibaghaee   I do not see any errors.

@rlopez  Thank you for reminding about  plots:-shadebetween  command. It appears only in Maple 2015 and I just did not know about this.

@mostafajani  For such functions better use  piecewise  command.

restart; 
f := proc(x) if is(x < 0) then x else x^2 end if end proc;
g := piecewise(x<0, x, x^2);

Examples of use:

plot('f'(x), x=-1..2);
plot(g(x), x=-1..2);
 

@Rouben Rostamian  Strange but somehow I forgot about  this easiest way.