# Solution for integral_0^t exp(A(s))x ds?

1. Dec 9, 2009

### uekstrom

Dear all,
do you know how to best calculate

$q(t) = \int_0^t \exp(A(s))v_0 ds$

where $A(s)$ is a low order matrix polynomial in s, and v_0 is a constant vector of suitable dimension? I can of course use a general ODE solver, but I want to understand how small perturbations in A affect the final result. In particular I want to use something like
$A(s) = A_1(1-s) + A_2s + A_{12}s(1-s),$
where the different A matrices are antisymmetric and do not generally commute (if they did commute the problem would not be very difficult).