Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
Matsulevich, S., Neittaanmäki, P., & Repin, S. (2013). Guaranteed error bounds for a class of Picard-Lindelöf iteration methods. In S. Repin, T. Tiihonen, & T. Tuovinen (Eds.), Numerical Methods for Differential Equations, Optimization, and Technological Problems. Dedicated to Professor P. Neittaanmäki on His 60th Birthday (pp. 175-189). Springer. Computational Methods in Applied Sciences, 27. https://doi.org/10.1007/978-94-007-5288-7_10
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Computational Methods in Applied SciencesDate
2013Copyright
© Springer Science+Business Media Dordrecht 2013
We present a new version of the Picard-Lindelof method for ordinary dif- ¨
ferential equations (ODEs) supplied with guaranteed and explicitly computable upper
bounds of an approximation error. The upper bounds are based on the Ostrowski
estimates and the Banach fixed point theorem for contractive operators. The estimates
derived in the paper take into account interpolation and integration errors
and, therefore, provide objective information on the accuracy of computed approximations.
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SpringerParent publication ISBN
978-94-007-5287-0Is part of publication
Numerical Methods for Differential Equations, Optimization, and Technological Problems. Dedicated to Professor P. Neittaanmäki on His 60th BirthdayISSN Search the Publication Forum
1871-3033Keywords
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