Validated solutions of initial value problems for parametric ODEs

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A Chebyshev interval method for nonlinear dynamic systems under uncertainty (2013, methodology): “Lin [20] proposed a VSPODE method which combined the two methods to solve ODEs with”
Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions (2013, methodology): “Lin proposed a validating solver for parametric ODE method [27] to solve interval ODE systems for obtaining sharper interval results.”
Nonlinear convex and concave relaxations for the solutions of parametric ODEs (2013, background): “Numerical techniques for generating state bounds may be found in [30, 31, 14, 32, 33, 34].”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “Both phases typically rely on a high-order Taylor expansion of the ODE solutions in time, and the enclosures are propagated by a variety of affine set-parameterization extensions (Berz and Makino, 2006; Lin and Stadtherr, 2007b; Neher et al., 2007).”
Deterministic Global Optimization for Parameter Estimation of Dynamic Systems (2006, background): “i ai ;1 if ai 13 ) The part of Xi to be retained is then Xi = Xi\ Ui + xi0 bi”