Construction and computation of variable coefficient sylvester differential problems

Abstract

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.