I have a 2688x1 matrix of ground acceleration data that I converted to a forcing function F (also a 2688x1 matrix) that I need to evaluate using duhamels integral. Since the forcing function can not be represented my a real expression numberical integration is required. Am needing to write a loop as seen on bottom of attached picture. Essentially to perform trapezoidal rule to return  structural motion (u).

Am looking for advice on how to write this loop in Maple.

I have attempted the for program in Maple per below with;

[F]:= Forcing Matrix 
[t]:= time step matrix

Assigned initial conditions sim to pic below

for i from 1..2688 do

added the functions sim to bottom of pic for Ai, Bi, and ui 

end do