Geodesic
On approximation of definite integrals by compound quadrature formulas using derivatives
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 88-104 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of computing a definite integral of a function for which the values of itself and the set of derivatives up to a given order at the points of the interval of integration are known is considered. Composite quadrature formulas are constructed that use the values of the function and its derivatives up to the m-th order inclusive. A representation of the remainder is obtained, expressed in terms of the derivative of the corresponding order and the number of nodal points. Examples of integration of the given functions with the study of the error and its estimation are given. A comparison is made with the known numerical methods and the Euler-Maclaurin formula, which showed increased accuracy and better convergence of the two-point integration method.
Keywords: quadrature formulas using derivatives, compound quadrature formula, remainder of integration, approximation error estimate, Euler-Maclaurin formula. 
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V. V. Shustov. On approximation of definite integrals by compound quadrature formulas using derivatives. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 88-104. http://geodesic.mathdoc.fr/item/VKAM_2021_34_1_a7/

[1] Berezin I. S., Metody vychisleniy, Fizmatlit, M., 1962, 464 pp. (in Russian)

[2] Bakhvalov N. S., Zhidkov N. P., Kobel'kov G. M., Chislennyye metody, Ucheb. posobiye, Nauka, M., 1987, 600 pp. (in Russian) | MR

[3] Verzhbitskiy V. M., Chislennyye metody, OOO Izdatel'skiy dom Oniks 21 vek, M., 2005, 400 pp. (in Russian)

[4] Volkov Ye. A., Chislennyye metody, Ucheb. posobiye dlya vuzov, Nauka, M., 1987, 248 pp. (in Russian)

[5] Khemming R. V., Chislennyye metody dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1972, 400 pp. (in Russian)

[6] Shakhov Yu. N., Deza Ye. I., Chislennyye metody, Uchebnoye posobiye, Knizhnyy dom Librokom, M., 2010, 248 pp. (in Russian) | MR

[7] Kalitkin N. N., Chislennyye metody, Uchebnoye posobiye, BKHV-Peterburg, SPb., 2011, 592 pp. (in Russian)

[8] Krylov V. I., Priblizhennoye vychisleniye integralov, Nauka, M., 1967, 500 pp. (in Russian) | MR

[9] Krylov V. I., Kvadraturnyye formuly, Nauka, M., 1988, 256 pp. (in Russian) | MR

[10] Fikhtengol'ts G. M., Kurs differentsial'nogo i integral'nogo ischisleniya, v. 2, Nauka, M., 1970, 800 pp. (in Russian)

[11] Shustov V. V., “O predstavlenii integralov znacheniyami funktsii i yeye proizvodnykh na osnove ispol'zovaniya dvukhtochechnykh mnogochlenov Ermita”, Teoriya operatorov, kompleksnyy analiz i matematicheskoye modelirovaniye, tezisy dokladov XIII Mezhd. nauchn. konf., Vladikavkaz, YUMI VNTS RAN, 2016, 85-87 (in Russian)

[12] Shustov V. V., “O priblizhenii funktsiy dvukhtochechnymi interpolyatsionnymi mnogochlenami Ermita”, Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki, 55:7 (2015), 1091-1108 (in Russian) | MR | Zbl

[13] Kudryavtsev L. D., Matematicheskii analiz, v. 1, Vysshaya shkola, M., 1970, 592 pp. (in Russian)

[14] Korn G., Korn T., Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov, Nauka, M., 1984, 832 pp. (in Russian)

[15] Grekhem R., Knut D., Patashnik O., Konkretnaya matematika. Osnovaniye informatiki, Mir, M., 1998, 703 pp. (in Russian) | MR

[16] Shustov V. V., “O predstavlenii integralov znacheniyami funktsii i yeye proizvodnykh na osnove ispol'zovaniya dvukhtochechnykh mnogochlenov Ermita”, Matematicheskiy forum. (Itogi nauki. Yug Rossii). YUMI RAN, 11 (2017), 113-122 (in Russian)

[17] Shustov V. V., “O predstavlenii opredelennykh integralov znacheniyami funktsii i yeye proizvodnykh”, Vladikavkazskiy matematicheskiy zhurnal, 22:2 (2020), 83-97 (in Russian) | MR