Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

Matsulevich, Svetlana; Neittaanmäki, Pekka; Repin, Sergey

doi:10.1007/978-94-007-5288-7_10

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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

Päivämäärä

2013

Oppiaine

Tietotekniikka Mathematical Information Technology

Tekijänoikeudet

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.

Julkaisija

Springer

Emojulkaisun ISBN

978-94-007-5287-0

Kuuluu julkaisuun

Numerical Methods for Differential Equations, Optimization, and Technological Problems. Dedicated to Professor P. Neittaanmäki on His 60th Birthday

ISSN Hae Julkaisufoorumista

1871-3033

Asiasanat

a posteriori estimates elliptic boundary value problems guaranteed error bounds Picard-Lindelöf methods inversio-ongelmat

DOI

https://doi.org/10.1007/978-94-007-5288-7_10

URI

http://urn.fi/URN:NBN:fi:jyu-201706283096

Julkaisu tutkimustietojärjestelmässä

https://converis.jyu.fi/converis/portal/detail/Publication/21748917

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