Geometric Series Bounds for the Local errors of Taylor Methods for Linear n-th-Order ODEs
نویسنده
چکیده
Interval Taylor methods for the validated solution of initial value problems for ODEs were introduced by Moore (1965a, 1965b, 1966). Lohner (1987, 1988, 1992) developed a comprehensive software package of an advanced interval Taylor method, which he applied successfully to many linear and nonlinear problems. But, as Lohner (1988) remarked, the step size of his method is limited by the step size for the explicit Euler method. Lohner (1995), Corliss & Rihm (1996) and Nedialkov (1999) have proposed modified versions of Lohner’s algorithm that remove this restriction. However, to the author’s knowledge these alternatives have not been extensively tested and have not been implemented in software for general IVPs.
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