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

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 form...

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Veröffentlicht in:	Czechoslovak Mathematical Journal 2023-12, Vol.73 (4), p.1175-1188
Hauptverfasser:	Tvrdá, Katarína, Novotný, Peter
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Analysis Computation Convex and Discrete Geometry Derivatives Differential equations Integrals Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Numerical integration Ordinary Differential Equations Quadratures
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Beschreibung
Zusammenfassung:	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.
ISSN:	0011-4642 1572-9141
DOI:	10.21136/CMJ.2023.0437-22