Computing continuous numerical solutions of matrix differential equations

In this paper, we construct analytical approximate solutions of initial value problems for the matrix differential equation X′(t) = A(t) X(t) + X(t) B(t) + L(t), with twice continuously differentiable functions A(t), B(t), and L(t), continuous. We determine, in terms of the data, the existence interval of the problem. Given an admissible error , we construct an approximate solution whose error is smaller than uniformly, in all the domain.