Article
| Title: | Modifications of Newton-Cotes formulas for computation of repeated integrals and derivatives (English) |
| Author: | Tvrdá, Katarína |
| Author: | Novotný, Peter |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1175-1188 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | repeated integral |
| Keyword: | Cauchy formula for repeated integration |
| Keyword: | quadrature |
| Keyword: | cubature |
| Keyword: | numerical differentiation |
| MSC: | 65D32 |
| DOI: | 10.21136/CMJ.2023.0437-22 |
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| Date available: | 2023-11-23T12:24:58Z |
| Last updated: | 2023-11-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151953 |
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| Reference: | [3] Burden, R. L., Faires, J. D.: Numerical Analysis.PWS Publishing Company, Boston (1993). Zbl 0788.65001 |
| Reference: | [4] Folland, G. B.: Advanced Calculus.Prentice Hall, Hoboken (2001). |
| Reference: | [5] Holoborodko, P.: Stable Newton-Cotes Formulas.Available at \brokenlink{http://www.holoborodko.com/pavel/numerical-methods/numerical-integration/{stable-newton-cotes-formulas/}}. |
| Reference: | [6] Janečka, A., Průša, V., Rajagopal, K. R.: Euler-Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range.Arch. Mech. 68 (2016), 3-25. Zbl 1338.74073, MR 3497874 |
| Reference: | [7] Selvam, V. K. M., Bindhu, K. R.: Application of double integration method and the Maxwell-Betti theorem for finding deflection in determinate flexural frames: A supplement note.J. Struct. Eng. 41 (2014), 420-431. |
| Reference: | [8] Tvrdá, K.: Solution of a high bridge pillar under wind effects taking into account the real properties of reinforced concrete.MATEC Web Conf. 313 (2020), 6 pages. 10.1051/matecconf/202031300008 |
| Reference: | [9] Tvrdá, K., Minárová, M.: Computation of definite integral over repeated integral.Tatra Mt. Math. Publ. 72 (2018), 141-154. Zbl 07031665, MR 3939444, 10.2478/tmmp-2018-0026 |
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