ValEncIA-IVP

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 18 articles , 1 standard article )

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  1. 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)
  2. Dzetkulič, Tomáš: Rigorous integration of non-linear ordinary differential equations in Chebyshev basis (2015)
  3. Feng, Zhiguang; Lam, James: On reachable set estimation of singular systems (2015)
  4. Villanueva, Mario E.; Houska, Boris; Chachuat, Beno^ıt: Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs (2015)
  5. Rauh, Andreas; Senkel, Luise; Auer, Ekaterina; Aschemann, Harald: Interval methods for real-time capable robust control of solid oxide fuel cell systems (2014)
  6. 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)
  7. Fazal, Qaisra; Neumaier, Arnold: Error bounds for initial value problems by optimization (2013)
  8. Scott, Joseph K.; Barton, Paul I.: Interval bounds on the solutions of semi-explicit index-one DAEs. I: Analysis (2013)
  9. Scott, Joseph K.; Barton, Paul I.: Interval bounds on the solutions of semi-explicit index-one DAEs. II: Computation (2013)
  10. Auer, Ekaterina; Rauh, Andreas: VERICOMP: A system to compare and assess verified IVP solvers (2012)
  11. Rauh, Andreas; Kersten, Julia; Auer, Ekaterina; Aschemann, Harald: Sensitivity-based feedforward and feedback control for uncertain systems (2012)
  12. Aschemann, H.; Minisini, J.; Rauh, A.: Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics (2010)
  13. Krasnochtanova, Irina; Rauh, Andreas; Kletting, Marco; Aschemann, Harald; Hofer, Eberhard P.; Schoop, Karl-Michael: Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties (2010)
  14. Rauh, Andreas; Minisini, Johanna; Hofer, Eberhard P.: Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamical systems with uncertainties (2010)
  15. Rump, Siegfried M.: Verification methods: rigorous results using floating-point arithmetic (2010)
  16. Freihold, Mareile; Hofer, Eberhard P.: Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems (2009)
  17. Rauh, Andreas; Brill, Michael; Günther, Clemens: A novel interval arithmetic approach for solving differential-algebraic equations with ValEncIA-IVP (2009)
  18. Auer, Ekaterina; Rauh, Andreas; Hofer, Eberhard P.; Luther, Wolfram: Validated modeling of mechanical systems with SmartMOBILE: Improvement of performance by ValEncIA-IVP (2008)