A new algorithm for computing the asymptotic solutions of a class of linear differential systems (Q1355761)

The linear differential system \[ Z'(x)= \rho(x)\{D+ R(x)\} Z(x),\qquad a\leq x< \infty \tag{\(*\)} \] is considered. Here, \(Z\) is an \(n\)-component vector, \(\rho\) is a real or complex scalar factor, \(D\) is a constant diagonal \(n\times n\)-matrix with distinct components and \(R\) is also an \(n\times n\)-matrix, \(R(x)\to 0\) as \(x\to\infty\). The paper reports on a new algorithm for computing asymptotic solutions to \((*)\) as well as for estimating and improving their error terms. A feature of the algorithm is the ability to accomodate periodic coefficients.