6533b852fe1ef96bd12ab809
RESEARCH PRODUCT
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
Svetlana MatculevichSergey RepinPekka Neittaanmäkisubject
Discrete mathematicsClass (set theory)Banach fixed-point theoremOdeguaranteed error boundsPicard-Lindelöf methodsinversio-ongelmatelliptic boundary value problemsPower iterationApproximation errorOrdinary differential equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematicsa posteriori estimatesObjective informationInterpolationMathematicsdescription
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. peerReviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |