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Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1175-1188
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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.
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.
DOI : 10.21136/CMJ.2023.0437-22
Classification : 65D32
Keywords: repeated integral; Cauchy formula for repeated integration; quadrature; cubature; numerical differentiation 
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Tvrdá, Katarína; Novotný, Peter. Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1175-1188. doi: 10.21136/CMJ.2023.0437-22

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