Approximate diagonalization in differential systems and an effective   algorithm for the computation of the spectral matrix
  This paper reports on recent work to compute the asymptotic solution of a n-th order ordinary differential equation. Symbolic methods are used to compute the asymptotics over a large region. Application is made to the computation of the Titchmarsh-Weyl M-matrix for the fourth order operator. 
B.M. Brown, M.S.P. Eastham, D.K.R. McCormack, W.D. Evans