Verified integration of linear nth order ODEs using large steps
The solution y(x) of an IVP for a linear ODE with analytic coefficient functions is represented as a power series. A high-order Taylor polynomial is used for an approximate numerical solution. The Taylor remainder series is rigorously estimated by some geometric series. 
 
The method has been implemented and tested on a computer. Guaranteed enclosures are achieved by taking into account all roundoff errors.