@Carl Love 

Yes it does, took me some time to understand the code but I works and does what I wanted. Thanks a lot!

@Carl Love 

This seems like an entirely new task but it is equivalent to my original problem. You can forget about the ODE problem, I think it should not be important here. I only need a procedure that implements the following steps and produces the output that I mention in this pdf:

num211_2.pdf

I tried to make it as clear as possible, but if there is anything unclear don't hesitate to ask

Thanks a ton!

@Carl Love 

I posted the question here: https://www.mapleprimes.com/questions/228742-Method-To-Approximate-Solution-Of-ODE?sq=228742

I also edited the pdf, the initital matrix M is constant.

@Carl Love 

Thanks a lot! That's exactly what I wanted and works perfectly.

I also got a second problem which is far beyond my maple skills. If you have some spare time I would really appreciate if you could have a look at it. I uploaded it as a pdf, but I can also post a image if you want.

num211.pdf