@Carl Love 

I think I've found an "easy" way to solve the geodetic equations numerically. It's nothing complicated, but this piece of code is crucial.

restart;
N := 4:
L:=[]:
build:= proc(j)
  local k;
  global L;
  L:=[]:
 
  for k from 2 to j do
    L:= [op(L), v[k]];
  end do;

  RETURN(L);
end proc:

for j from 2 to N-1 do
  for i from 2 to j do
   if nops(L) = 0
    then
      # print(nops(L)); # Debug only
      # I need this here, but how to do ?
      nops(L); # <- Not working
    end if;
    
    build(i);
    
    if nops(L) > 0
    then
      for s from 1 to nops(L) do
        # print(L[s]); # Debug only
        # I need this here, but how to do ?
        L[s]; # <- Not working
      end do;
    end if;
  end do;
end do;

@acer 

At first I thought it was an index problem. Later I realized that this was not the case. The issue is beyond me, I don't know how to deal with it - maybe the solution is trivial, but I don't see it.

I explained everything in Maple worksheet.

Test.mw

@jganding 

Problem solved! Thanks to you, everything works as it should! Thank you!

@jganding 

Thank you very, very, very much for your in-depth analysis of the problem and comprehensive comment and description. Your comments are already starting to result in a more correct implementation of the issue. I must admit that I never thought that my definition of odeSys and initial conditions could be the cause of all the "confusion". That's why I thank you even more for your help. Thank you!

Best regards!

@acer 

Thank you very much for your reply and code. Now I'm analyzing the whole thing. Then I'll work on my code. When I do this, I will write to you again, send you my code and provide explanations that are still missing in the whole matter. Please be patient. I will reply as soon as possible.

Very warm regards.

@acer These are things I need to work on. Thank you very much for these comments.

@mmcdara 

Thank you very much!

I will analyze your code. This will be an enlightening analysis for me.

Best regards!

@Kitonum 

Thank you, it works. however the problem is more complex as in my worksheet - uploaded in my second post.. Could I ask you for help in solving the problem?