Computing continuous numerical solutions of matrix differential equations

In this paper, the authors 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. They 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.