VALENCIA-IVP: A Comparison with Other Initial Value Problem Solvers Validated integration of ordinary differential equations with uncertain initial conditions and uncertain parameters is important for many practical applications. If guaran- teed bounds for the uncertainties are known, interval meth- ods can be applied to obtain validated enclosures of all states. However, validated computations are often affected by overestimation, which, in naive implementations, might even lead to meaningless results. Parallelepiped and QR preconditioning of the state equations, Taylor model arith- metic, as well as simulation techniques employing split- ting and merging routines are a few existing approaches for reduction of overestimation. In this paper, the recently developed validated solver VALENCIA-IVP and several methods implemented there for reduction of overestimation are described. Furthermore, a detailed comparison of this solver with COSY VI and VNODE, two of the most well- known validated ODE solvers, is presented. Simulation re- sults for simplified system models in mechanical and bio- process engineering show specific properties, advantages, and limitations of each tool.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 29 articles , 1 standard article )

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  1. Kapela, Tomasz; Mrozek, Marian; Wilczak, Daniel; Zgliczyński, Piotr: CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems (2021)
  2. Bünger, Florian: A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB (2020)
  3. Rauh, Andreas; Kersten, Julia; Aschemann, Harald: Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer (2020)
  4. Konečný, Michal; Taha, Walid; Bartha, Ferenc A.; Duracz, Jan; Duracz, Adam; Ames, Aaron D.: Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point (2016)
  5. Pérez-Galván, Carlos; Bogle, I. David L.: Dynamic global optimization methods for determining guaranteed solutions in chemical engineering (2016)
  6. Walawska, Irmina; Wilczak, Daniel: An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs (2016)
  7. Dzetkulič, Tomáš: Rigorous integration of non-linear ordinary differential equations in Chebyshev basis (2015)
  8. Feng, Zhiguang; Lam, James: On reachable set estimation of singular systems (2015)
  9. Villanueva, Mario E.; Houska, Boris; Chachuat, Benoît: Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs (2015)
  10. Rauh, Andreas; Senkel, Luise; Auer, Ekaterina; Aschemann, Harald: Interval methods for real-time capable robust control of solid oxide fuel cell systems (2014)
  11. Auer, Ekaterina; Kiel, Stefan; Rauh, Andreas: A verified method for solving piecewise smooth initial value problems (2013)
  12. Dötschel, Thomas; Auer, Ekaterina; Rauh, Andreas; Aschemann, Harald: Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control (2013) ioport
  13. Fazal, Qaisra; Neumaier, Arnold: Error bounds for initial value problems by optimization (2013)
  14. Obaid, Hasim A.; Ouifki, Rachid; Patidar, Kailash C.: An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection (2013)
  15. Scott, Joseph K.; Barton, Paul I.: Interval bounds on the solutions of semi-explicit index-one DAEs. I: Analysis (2013)
  16. Scott, Joseph K.; Barton, Paul I.: Interval bounds on the solutions of semi-explicit index-one DAEs. II: Computation (2013)
  17. Auer, Ekaterina; Rauh, Andreas: VERICOMP: A system to compare and assess verified IVP solvers (2012)
  18. Rauh, Andreas; Aschemann, Harald: Parameter identification and observer-based control for distributed heating systems - the basis for temperature control of solid oxide fuel cell stacks (2012)
  19. Rauh, Andreas; Kersten, Julia; Auer, Ekaterina; Aschemann, Harald: Sensitivity-based feedforward and feedback control for uncertain systems (2012)
  20. Aschemann, H.; Minisini, J.; Rauh, A.: Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics (2010)

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