Abstract
A Method for Producing Verified Results for Two-Point Boundary Value Problems. This paper presents algorithms for solving second order two-point boundary value problems which yield existence proofs and two-sided bounds (EB-algorithms) The algorithms are composed of two numerical procedures as sub-algorithms, an approximation procedure A for calculating approximate solutions of certain boundary value problems, and an estimation procedure E for calculating bounds of certain continuous functions. Conditions (on the given boundary value problems) are formulated such that the EB-algorithms can be carried out, if these conditions are satisfied and procedures A and E of sufficient accuracy are available.
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