GMRES for oscillatory matrix-valued differential equations - Olver, S (Springer (ICOSAHOM conference proceeding), 2009)
We investigate the use of Krylov subspace methods to solve linear, oscillatory ODEs. When we apply a Krylov subspace method to a properly formulated equation, we retain the asymptotic accuracy of the asymptotic expansion whilst converging to the exact solution. We will demonstrate the effectiveness of this method by computing Error and Mathieu functions.