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Displaying similar documents to “On the error estimation in numerical methods”

Multiple-Precision Correctly rounded Newton-Cotes quadrature

Laurent Fousse (2007)

RAIRO - Theoretical Informatics and Applications

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Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics.
We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds...

Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives

Katarína Tvrdá, Peter Novotný (2023)

Czechoslovak Mathematical Journal

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Standard algorithms for numerical integration are defined for simple integrals. Formulas for computation of repeated integrals and derivatives for equidistant domain partition based on modified Newton-Cotes formulas are derived. We compare usage of the new formulas with the classical quadrature formulas and discuss possible application of the results to solving higher order differential equations.