A taylor series methodology for analyzing the effects of process variation on circuit operation
Proceedings of the 19th ACM Great Lakes symposium on VLSI
Verified Solution Method for Population Epidemiology Models with Uncertainty
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
Chebyshev interpolation polynomial-based tools for rigorous computing
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Effective bounds for P-recursive sequences
Journal of Symbolic Computation
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs
Applied Numerical Mathematics
Rigorous polynomial approximation using taylor models in Coq
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Bounds on the reachable sets of nonlinear control systems
Automatica (Journal of IFAC)
Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets
Proceedings of the 16th international conference on Hybrid systems: computation and control
Flow*: an analyzer for non-linear hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Convergence analysis of Taylor models and McCormick-Taylor models
Journal of Global Optimization
Improved relaxations for the parametric solutions of ODEs using differential inequalities
Journal of Global Optimization
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Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods are able to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or the integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz and his coworkers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. We analyze Taylor model based integration of ODEs and compare Taylor model methods with traditional enclosure methods for IVPs for ODEs.