Centrum voor Wiskunde en Informatica
                                     REPORTRAPPORT
                Test Set for Initial Value Problem Solvers
                W.M. Lioen, J.J.B. de Swart
                Modelling, Analysis and Simulation (MAS)
                MAS-R9832 December 1998
         Report MAS-R9832
         ISSN 1386-3703
         CWI
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Test Set for Initial Value Problem Solvers
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Walter M. Lioen
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands (Walter.Lioen@cwi.nl)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Jacques J.B. de Swart
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands (Jacques.de.Swart@cwi.nl) &
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Paragon Decision Technology, PO Box 3277, 2001 DG Haarlem, The Netherlands (jacques@paragon.nl)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Release 2.0 December 1998
                                                                                                                                                                                                                                                                                                                                                                                                                                                       ABSTRACT
                                                                                                                                                                                                                                                                                                                                                                                                                                                       The CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differ-
                                                                                                                                                                                                                                                                                                                                                                                                                                                       ential equations. This test set can both decrease the effort for the code developer to test his software in a reliable
                                                                                                                                                                                                                                                                                                                                                                                                                                                       way, and cross the bridge between the application field and numerical mathematics. This document contains
                                                                                                                                                                                                                                                                                                                                                                                                                                                       the descriptive part of the test set. It describes the test problems and their origin, and reports on the behavior
                                                                                                                                                                                                                                                                                                                                                                                                                                                       of a few state-of-the-art solvers on these problems. The latest version of this document and the software part
                                                                                                                                                                                                                                                                                                                                                                                                                                                       of the test set is available via the world wide web at http://www.cwi.nl/cwi/projects/IVPtestset/.
                                                                                                                                                                                                                                                                                                                                                                                                                                                       The software part serves as a platform on which one can test the performance of a solver on a particular test
                                                                                                                                                                                                                                                                                                                                                                                                                                                       problem oneself. Instructions how to use this software are in this paper as well. The idea to develop this test
                                                                                                                                                                                                                                                                                                                                                                                                                                                       set was discussed at the workshop ODE to NODE, held in Geiranger, Norway, 19–22 June 1995.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                       1991 Mathematics Subject Classification: Primary: 65Y20, Secondary: 65-04, 65C20, 65L05.
                                                                                                                                                                                                                                                                                                                                                                                                                                                       1991 Computing Reviews Classification System: G.1.7, G.4.
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Keywords and Phrases: test problems, software, IVP, IDE, ODE, DAE.
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Note: The maintenance of the test set belongs to the project MAS2.2: ‘Parallel Software for Implicit Differential
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Equations’.
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Acknowledgements: Thisworkissupported financially by the ‘Technologiestichting STW’ (Dutch Foundation for
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Technical Sciences), grants no. CWI.2703, CWI.4533. The use of supercomputer facilities was made possible by
                                                                                                                                                                                                                                                                                                                                                                                                                                                       the ‘Stichting Nationale Computerfaciliteiten’ (National Computing Facilities Foundation, NCF), with financial
                                                                                                                                                                                                                                                                                                                                                                                                                                                       support from the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek’ (Netherlands Organization for
                                                                                                                                                                                                                                                                                                                                                                                                                                                       Scientific Research, NWO). We thank all contributors to this test set, without whom it would not be possible
                                                                                                                                                                                                                                                                                                                                                                                                                                                       to collect problems from such a wide variety of application fields.