Abstract
One can reduce the uncertainty in the quality of an approximate solution of an ordinary differential equation (ODE) by implementing methods which have a more rigorous error control strategy and which deliver an approximate solution that is much more likely to satisfy the expectations of the user. We have developed such a class of ODE methods as well as a collection of software tools that will deliver a piecewise polynomial as the approximate solution and facilitate the investigation of various aspects of the problem that are often of as much interest as the approximate solution itself. We will introduce measures that can be used to quantify the reliability of an approximate solution and discuss how one can implement methods that, at some extra cost, can produce very reliable approximate solutions and therefore significantly reduce the uncertainty in the computed results.
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© 2012 IFIP International Federation for Information Processing
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Enright, W.H. (2012). Reducing the Uncertainty When Approximating the Solution of ODEs. In: Dienstfrey, A.M., Boisvert, R.F. (eds) Uncertainty Quantification in Scientific Computing. WoCoUQ 2011. IFIP Advances in Information and Communication Technology, vol 377. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32677-6_18
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DOI: https://doi.org/10.1007/978-3-642-32677-6_18
Publisher Name: Springer, Berlin, Heidelberg
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