Czechoslovak Mathematical Journal, Vol. 73, No. 4, pp. 1175-1188, 2023
Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
Katarína Tvrdá, Peter Novotný
Received October 2, 2022. Published online March 24, 2023.
Abstract: 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.
Keywords: repeated integral; Cauchy formula for repeated integration; quadrature; cubature; numerical differentiation
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Affiliations: Katarína Tvrdá, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia, e-mail: katarina.tvrda@stuba.sk; Peter Novotný (corresponding author), University of Žilina, Univerzitná 8215/1, 010 26 Žilina, Slovakia e-mail: peter.novotny@fri.uniza.sk
