Abstract
Methods of interval mathematics are used to find upper and lower bounds for the solution of two-point boundary-value problems at discrete mesh points. They include interval versions of shooting and of finite-difference techniques for linear and non-linear differential equations of second order, and of finite-difference methods for Sturm-Liouville eigenvalue problems.
Good results are obtained whenever the difficulties of dependency-width can be avoided, and particularly for the finite-difference method when the associated matrix is anM matrix.
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Fox, L., Valenca, M.R. Some experiments with interval methods for two-point boundary-value problems in ordinary differential equations. BIT 20, 67–82 (1980). https://doi.org/10.1007/BF01933587
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DOI: https://doi.org/10.1007/BF01933587