ValEncIA-IVP swMATH ID: 4846 Software Authors: Andreas Rauh; Eberhard P. Hofer; Ekaterina Auer Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=1338721 Related Software: ValEncIA; Cosy; FADBAD++; SmartMobile; VNODE; PROFIL/BIAS; INTLAB; RODES; kv; MPFR; Matlab; TADIFF; Flow*; CAPD DynSys; CAPD; ODEIntegrator; INTOPT_90; VERICOMP; C-XSC; MOBILE Cited in: 30 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Validated modeling of mechanical systems with SmartMOBILE: Improvement of performance by ValEncIA-IVP. Zbl 1165.65307Auer, Ekaterina; Rauh, Andreas; Hofer, Eberhard P.; Luther, Wolfram 2008 all top 5 Cited by 45 Authors 13 Rauh, Andreas 7 Aschemann, Harald 6 Auer, Ekaterina 5 Hofer, Eberhard P. 4 Minisini, Johanna 3 Wilczak, Daniel 2 Barton, Paul I. 2 Kapela, Tomasz 2 Kersten, Julia 2 Luther, Wolfram Jérôme 2 Scott, Joseph K. 2 Zgliczyński, Piotr 1 Ames, Aaron D. 1 Bartha, Ferenc Ágoston 1 Brill, Michael H. 1 Bünger, Florian 1 Chachuat, Benoît 1 Damers, Julien 1 Duracz, Adam 1 Duracz, Jan 1 Dzetkulič, Tomáš 1 Fazal, Qaisra 1 Feng, Zhiguang 1 Freihold, Mareile 1 Günther, Clemens 1 Houska, Boris 1 Jaulin, Luc 1 Kiel, Stefan 1 Kletting, Marco 1 Konečný, Michal 1 Krasnochtanova, Irina 1 Lam, James 1 Mrozek, Marian 1 Neumaier, Arnold 1 Obaid, Hasim A. 1 Ouifki, Rachid 1 Patidar, Kailash C. 1 Pérez-Galván, Carlos 1 Rohou, Simon 1 Rump, Siegfried Michael 1 Schoop, Karl-Michael 1 Senkel, Luise 1 Taha, Walid 1 Villanueva, Mario Eduardo 1 Walawska, Irmina all top 5 Cited in 17 Serials 6 International Journal of Applied Mathematics and Computer Science 2 Automatica 2 Computing 2 Numerische Mathematik 2 Journal of Computer and Systems Sciences International 2 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Control 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Journal of Global Optimization 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 Soft Computing 1 Mathematical and Computer Modelling of Dynamical Systems 1 Acta Numerica 1 Mathematics in Computer Science 1 Nonlinear Analysis. Hybrid Systems all top 5 Cited in 11 Fields 21 Numerical analysis (65-XX) 16 Systems theory; control (93-XX) 9 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Operations research, mathematical programming (90-XX) 3 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year