Abstract
The Godess (Generic Ordinary Differential Equations Solving System) Project aims at development of an object-oriented solver for initial value problems. In this project, the use of object-oriented techniques has been instrumental in development, testing, evaluation and verification of methods and control strategies. Based on comparisons with traditional solvers, we find that Godess is competitive with respect to accuracy and computational speed. These experiments demonstrate that this very generic solver is of real practical value.
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References
J. J. B. de Swart. Test set for IVP solver. http://www.cwi.nl/cwi/projects/IVPtestset.html, 1995.
J. J. B. de Swart, W. A. van der Veen, and B. P. Sommeijer. Test set for IVPODE and IVPDAE solvers. Technical report, CWI, 1995.
J. Eborn. Modelling and simulation of an industrial control loop with friction. Master’s thesis, Lund Institute of Technology, March 1994.
C. Führer and B. J. Leimkuhler. Numerical solution of differential-algebraic equations for constrained mechanical motion. Numerische Mathematik, 59:55–69, 1991.
K. Gustafsson. Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods. ACM TOMS,17(4):533–554, December 1991.
K. Gustafsson. Control of Error and Convergence in ODE Solvers. PhD thesis, Lund Institute of Technology, 1992.
K. Gustafsson. Object oriented implementation of software for solving ordinary differential equations. In OON-SКI’93, P.O Box 2328, Corvallis, OR 97339, 1993. Rogue Wave Software.
K. Gustafsson. Object-oriented implementation of software for solving ordinary differential equations. Scientific Programming, 2:217–225, 1993.
K. Gustafsson. Control theoretic techniques for stepaize selection in implicit Runge-Kutta methods. ACM TOMS, 21(4):496–517, December 1994.
K. Gustafsson, M. Lundh, and G. Söderlind. A PI stepsize control for the numerical solution of ordinary differential equations. BIT, 28(2):270–287, 1988.
K. Gustafsson and G. Söderlind. Control strategies for the iterative solution of nonlinear equations in ODE solvers. SIAM Journal on Scientific and Statistical Computing, Jan 1997.
N. Houbak, S. P. Nørsett, and P. G. Thomsen. Displacement or residual test in the application of implicit methods for stiff problems. IMA Journal of Numerical Analysis, 5:297–305, 1985.
E. Hairer, S.P. Nøsett, and G. Wanner. Solving Ordinary Differential Equations II. Springer Verlag, 2nd edition, 1993.
E. Hairer and G. Wanner. Solving Ordinary Differential Equations II. Spring Verlag, Berlin, 2nd edition, 1996.
A. D. Jensen. An object-oriented platform for dynamic simulation. Master’s thesis, Denmark Technical University, Institute of Mathematical Modelling, DK-2800 Lyngby Denmark, 1994. IMM-EKS-1994–47.
A. Kvwrnø. More, and to be hoped, better DIRK methods for the solution of stiff ODEs. Technical report, Mathematical Sciences Div., Norwegian Institute of Technology, Trondheim, 1992.
Netlib ODE solvers. http://www.netlib.org/ode/.
Netlib ODEPACK. http://www.netlib.org/odepack/.
S. P. Norsett and P. G. Thomsen. Switching between Newton and fix-point iteration for implicit ODE-solvers. BIT, 26:339–348, 1986.
H. Olsson. Practical implementation of Runge-Kutta methods for initial value problems. Licentiate Thesis, Lund Institute of Technology, December 1995.
H. Olsson. Object oriented solvers for initial value problems. In OONSCI’96, 1996. To appear.
H. Olsson and G. Söderlind. Stage value predictors and efficient Newton iterations in implicit Runge-Kutta methods. Technical Report LU-CS-TR:96–182, Department of Computer Science, Lund University, P.O. Box 118, S-221 00 Lund, Sweden, 1996. Also submitted for publication.
J. Rumbaugh, M. Blaha, F. Eddy W. Premerlani, and W. Lorensen. Object-Oriented Modeling and Design. Prentice Hall, 1993.
K. J. Åström and B. Wittenmark. Computer-Controlled Systems. Prentice-Hall, 2nd edition, 1990.
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Olsson, H. (1997). Object-Oriented Solvers for Initial Value Problems. In: Arge, E., Bruaset, A.M., Langtangen, H.P. (eds) Modern Software Tools for Scientific Computing. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1986-6_2
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DOI: https://doi.org/10.1007/978-1-4612-1986-6_2
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