An enclosure method for the solution of linear odes with polynomial coefficients

The solution y(x) of an initial value problem for a linear ODE with polynomial coefficients is represented as a power series. The remainder series is bounded by a geometric series, resulting in close bounds for y. The method has been implemented on a computer, where highly accurate results are attained with the staggered correction technique. For guaranteed enclosures on the computer, all roundoff errors have to be taken into account in the course of computation.

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