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). Computational Methods in Applied Sciences, 27. Berlin: Springer. doi:10.1007/978-94-007-5288-7_10
Published inComputational Methods in Applied Sciences;27
© 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.
Is part of publicationNumerical Methods for Differential Equations, Optimization, and Technological Problems. Dedicated to Professor P. Neittaanmäki on His 60th Birthday
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