Construction and computation of variable coefficient sylvester differential problems

In this paper, initial value problems for Sylvester differential equations X′(t) = A(t)X(t) + X(t)B(t) + F(t), with analytic matrix coefficients are considered. First, an exact series solution of the problem is obtained. Given a bounded domain Ω and an admissible error ε, a finite analytic-numerical series solution is constructed, so that the error with respect to the exact series solution is uniformly upper bounded by ε in Ω. An iterative procedure for the construction of the approximate solutions is included.