Abstract
Validated methods for initial value problems for ordinary differential equations produce bounds that are guaranteed to contain the true solution of a problem. When computing such bounds, these methods verify that a unique solution to the problem exists in the interval of integration and compute a priori bounds for the solution in this interval. A major difficulty in this verification phase is how to take as large a stepsize as possible, subject to some tolerance requirement. We propose a high-order enclosure method for proving existence and uniqueness of the solution and computing a priori bounds.
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Nedialkov, N.S., Jackson, K.R. & Pryce, J.D. An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE. Reliable Computing 7, 449–465 (2001). https://doi.org/10.1023/A:1014798618404
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DOI: https://doi.org/10.1023/A:1014798618404