COMPUTING CONTINUOUS NUMERICAL-SOLUTIONS OF MATRIX DIFFERENTIAL-EQUATIONS

In this paper, we construct analytical approximate solutions of initia l 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, t he existence interval of the problem. Given an admissible error epsilo n, we construct an approximate solution whose error is smaller than ep silon uniformly, in all the domain.