Abstract
Implicit interval methods of Runge–Kutta and Adams–Moulton type for solving the initial value problem are proposed. It can be proved that the exact solution of the problem belongs to interval-solutions obtained by the considered methods. Furthermore, it is possible to estimate the widths of interval-solutions.
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Marciniak, A. Implicit Interval Methods for Solving the Initial Value Problem. Numerical Algorithms 37, 241–251 (2004). https://doi.org/10.1023/B:NUMA.0000049471.81341.60
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DOI: https://doi.org/10.1023/B:NUMA.0000049471.81341.60