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Journal articles on the topic 'Numerical integration'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Tabsum, B. "Python for Numerical Integration." International Journal of Science and Research (IJSR) 12, no. 5 (2023): 1801–5. http://dx.doi.org/10.21275/mr23521182224.

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2

Matušů, Josef, Gejza Dohnal, and Martin Matušů. "On one method of numerical integration." Applications of Mathematics 36, no. 4 (1991): 241–63. http://dx.doi.org/10.21136/am.1991.104464.

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3

Zadiraka, V. K., L. V. Luts, and I. V. Shvidchenko. "Optimal Numerical Integration." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 47–64. http://dx.doi.org/10.34229/2707-451x.20.4.4.

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Introduction. In many applied problems, such as statistical data processing, digital filtering, computed tomography, pattern recognition, and many others, there is a need for numerical integration, moreover, with a given (often quite high) accuracy. Classical quadrature formulas cannot always provide the required accuracy, since, as a rule, they do not take into account the oscillation of the integrand. In this regard, the development of methods for constructing optimal in accuracy (and close to them) quadrature formulas for the integration of rapidly oscillating functions is rather important

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4

Hochbruck, Marlis, Christian Lubich, Robert McLachlan, and Jesús María Sanz-Serna. "Geometric Numerical Integration." Oberwolfach Reports 18, no. 2 (2022): 943–99. http://dx.doi.org/10.4171/owr/2021/17.

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5

Elliott, David, H. Brass, and G. Hammerlin. "Numerical Integration IV." Mathematics of Computation 64, no. 210 (1995): 901. http://dx.doi.org/10.2307/2153467.

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6

Faou, Erwan, Ernst Hairer, Marlis Hochbruck, and Christian Lubich. "Geometric Numerical Integration." Oberwolfach Reports 13, no. 1 (2016): 869–948. http://dx.doi.org/10.4171/owr/2016/18.

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7

Clegg, D. B., and A. N. Richmond. "Perfect numerical integration." International Journal of Mathematical Education in Science and Technology 18, no. 4 (1987): 519–25. http://dx.doi.org/10.1080/0020739870180403.

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8

Dyer, Stephen, and Justin Dyer. "bythenumbers - Numerical integration." IEEE Instrumentation & Measurement Magazine 11, no. 2 (2008): 47–49. http://dx.doi.org/10.1109/mim.2008.4483733.

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9

G., W., H. Brass, and G. H. Hammerlin. "Numerical Integration III." Mathematics of Computation 53, no. 187 (1989): 451. http://dx.doi.org/10.2307/2008381.

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10

Burk, Frank. "Numerical Integration via Integration by Parts." College Mathematics Journal 17, no. 5 (1986): 418. http://dx.doi.org/10.2307/2686254.

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11

Burk, Frank. "Numerical Integration via Integration by Parts." College Mathematics Journal 17, no. 5 (1986): 418–22. http://dx.doi.org/10.1080/07468342.1986.11972993.

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12

Obradovic, Dragan, Lakshmi Narayan Mishra, and Vishnu Narayan Mishra. "Numerical Differentiation and Integration." JOURNAL OF ADVANCES IN PHYSICS 19 (January 25, 2021): 1–5. http://dx.doi.org/10.24297/jap.v19i.8938.

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There are several reasons why numerical differentiation and integration are used. The function that integrates f (x) can be known only in certain places, which is done by taking a sample. Some supercomputers and other computer applications sometimes need numerical integration for this very reason. The formula for the function to be integrated may be known, but it may be difficult or impossible to find the antiderivation that is an elementary function. One example is the function f (x) = exp (−x2), an antiderivation that cannot be written in elementary form. It is possible to find antiderivatio

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13

Chen, Chuanmiao, Michal Křížek, and Liping Liu. "Numerical Integration over Pyramids." Advances in Applied Mathematics and Mechanics 5, no. 03 (2013): 309–20. http://dx.doi.org/10.4208/aamm.12-m12110.

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AbstractPyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method. In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.

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14

Bland, J. A., and H. V. Smith. "Numerical Methods of Integration." Mathematical Gazette 79, no. 484 (1995): 244. http://dx.doi.org/10.2307/3620126.

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15

S., F., and H. V. Smith. "Numerical Methods of Integration." Mathematics of Computation 64, no. 210 (1995): 900. http://dx.doi.org/10.2307/2153466.

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16

Arthur, D. W., Philip J. Davis, and Philip Rabinowitz. "Methods of Numerical Integration." Mathematical Gazette 70, no. 451 (1986): 70. http://dx.doi.org/10.2307/3615859.

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17

Jacka, K., and David Lewin. "Numerical measures of integration." Journal of Advanced Nursing 11, no. 6 (1986): 679–85. http://dx.doi.org/10.1111/j.1365-2648.1986.tb03385.x.

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18

Balmino, G., and J. B. Harriot. "Numerical integration techniques revisited." manuscripta geodaetica 15, no. 1 (1990): 1–10. http://dx.doi.org/10.1007/bf03655383.

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19

Voronin, S. M., and V. I. Skalyga. "On numerical integration algorithms." Izvestiya: Mathematics 60, no. 5 (1996): 887–91. http://dx.doi.org/10.1070/im1996v060n05abeh000084.

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20

Schmee, Josef. "Tables for Numerical Integration." Technometrics 27, no. 1 (1985): 90–91. http://dx.doi.org/10.1080/00401706.1985.10488025.

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21

Laue, Hans. "Elementary numerical integration methods." American Journal of Physics 56, no. 9 (1988): 849–50. http://dx.doi.org/10.1119/1.15441.

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22

Valliappan, S., and K. K. Ang. "? method of numerical integration." Computational Mechanics 5, no. 5 (1989): 321–36. http://dx.doi.org/10.1007/bf01047049.

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23

Xin, Wu, and Huang Tian-yi. "Constraints and numerical integration." Chinese Astronomy and Astrophysics 29, no. 1 (2005): 81–91. http://dx.doi.org/10.1016/j.chinastron.2005.01.008.

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24

Huang, Xiaowei, Chuansheng Wu, and Jun Zhou. "Numerical differentiation by integration." Mathematics of Computation 83, no. 286 (2013): 789–807. http://dx.doi.org/10.1090/s0025-5718-2013-02722-6.

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25

Monahan, John F., Philip J. Davis, and Philip Rabinowitz. "Methods of Numerical Integration." Journal of the American Statistical Association 80, no. 392 (1985): 1081. http://dx.doi.org/10.2307/2288607.

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26

S., F., Philip J. Davis, and Philip Rabinowitz. "Methods of Numerical Integration." Mathematics of Computation 46, no. 174 (1986): 760. http://dx.doi.org/10.2307/2008014.

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27

Kalaida, A. F. "Matrix numerical integration algorithm." Journal of Mathematical Sciences 69, no. 6 (1994): 1369–78. http://dx.doi.org/10.1007/bf01250578.

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28

Hashish, H., S. H. Behiry, and N. A. El-Shamy. "Numerical integration using wavelets." Applied Mathematics and Computation 211, no. 2 (2009): 480–87. http://dx.doi.org/10.1016/j.amc.2009.01.084.

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29

Fukushima, Toshio, and Toshimichi Shirai. "Numerical Convolution Method in Time Domain and Its Application to Nonrigid Earth Nutation Theory." International Astronomical Union Colloquium 178 (2000): 595–605. http://dx.doi.org/10.1017/s0252921100061765.

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AbstractWe developed a numerical method to incorporate nonrigid effects into a nutation theory of the rigid Earth. Here we assume that the nonrigid effects are based on a linear response theory and its transfer function is expressed as a rational function of frequency. The method replaces the convolution of the transfer function in the frequency domain by the corresponding integro-differential operations in the time domain numerically; namely multiplying the polynomial in the frequency domain by the numerical differentiations in the time domain and multiplying the fractions in the frequency do

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30

Kim, Kyung Yong, and Uk Hyun Cho. "Approximating Bifactor IRT True-Score Equating With a Projective Item Response Model." Applied Psychological Measurement 44, no. 3 (2019): 215–18. http://dx.doi.org/10.1177/0146621619885903.

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Item response theory (IRT) true-score equating for the bifactor model is often conducted by first numerically integrating out specific factors from the item response function and then applying the unidimensional IRT true-score equating method to the marginalized bifactor model. However, an alternative procedure for obtaining the marginalized bifactor model is through projecting the nuisance dimensions of the bifactor model onto the dominant dimension. Projection, which can be viewed as an approximation to numerical integration, has an advantage over numerical integration in providing item para

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31

Abdulle, Assyr. "The role of numerical integration in numerical homogenization." ESAIM: Proceedings and Surveys 50 (March 2015): 1–20. http://dx.doi.org/10.1051/proc/201550001.

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32

Murphy, Robin. "103.45 Improving elementary numerical integration using numerical differentiation." Mathematical Gazette 103, no. 558 (2019): 548–56. http://dx.doi.org/10.1017/mag.2019.127.

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33

Holloway, Damien Scott. "Numerical stabilisation of motion integration." ANZIAM Journal 49 (July 16, 2007): 249. http://dx.doi.org/10.21914/anziamj.v48i0.51.

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34

Bakirov, N. K., and I. R. Gallyamov. "Comparison of numerical integration formulas." Russian Mathematics 54, no. 12 (2010): 1–16. http://dx.doi.org/10.3103/s1066369x10120017.

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35

Malmquist, Jens, and Robert Strichartz. "Numerical integration for fractal measures." Journal of Fractal Geometry 5, no. 2 (2018): 165–226. http://dx.doi.org/10.4171/jfg/60.

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36

Bartoš, Erik. "Numerical multidimensional integration with PyMikor." Computer Physics Communications 270 (January 2022): 108149. http://dx.doi.org/10.1016/j.cpc.2021.108149.

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37

Assouline, F., and P. Lailly. "Numerical Integration for Kirchhoff Migration." Oil & Gas Science and Technology 58, no. 3 (2003): 385–412. http://dx.doi.org/10.2516/ogst:2003024.

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38

Rees, W. G. "Numerical integration of orbital motion." European Journal of Physics 6, no. 4 (1985): 302–6. http://dx.doi.org/10.1088/0143-0807/6/4/017.

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39

Ginestar, D., G. Verdú, and J. March-Leuba. "Thermohydraulics Oscillations and Numerical Integration." Nuclear Science and Engineering 140, no. 2 (2002): 172–80. http://dx.doi.org/10.13182/nse02-a2253.

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40

Balkir, S., M. Yanilmaz, and M. Plonus. "Numerical integration using Bezier splines." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 13, no. 6 (1994): 737–45. http://dx.doi.org/10.1109/43.285248.

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41

Treutler, Oliver, and Reinhart Ahlrichs. "Efficient molecular numerical integration schemes." Journal of Chemical Physics 102, no. 1 (1995): 346–54. http://dx.doi.org/10.1063/1.469408.

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42

Soper, Davison E. "QCD Calculations by Numerical Integration." Physical Review Letters 81, no. 13 (1998): 2638–41. http://dx.doi.org/10.1103/physrevlett.81.2638.

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43

de Doncker, Elise, Ajay Gupta, and Rodger R. Zanny. "Large-scale parallel numerical integration." Journal of Computational and Applied Mathematics 112, no. 1-2 (1999): 29–44. http://dx.doi.org/10.1016/s0377-0427(99)00210-1.

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44

Smith, Harry V. "Numerical integration — a different approach." Mathematical Gazette 90, no. 517 (2006): 21–24. http://dx.doi.org/10.1017/s0025557200178994.

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In common with, I suspect, many people the author does not have access to the NAG library and so, when I was asked recently to calculate the value of the integralcorrect to 10 decimal places my first reaction was to try several different calculators as well as several mathematical software packages. On doing so it was disappointing to find they either gave widely differing values such as 7.9065200767, 4.1317217452 or 0.9174196842 or an error message indicating that the method had not converged.

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45

de Doncker, Elise. "Methods for enhancing numerical integration." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 502, no. 2-3 (2003): 358–63. http://dx.doi.org/10.1016/s0168-9002(03)00443-1.

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46

Soper, Davison E. "QCD calculations by numerical integration." Nuclear Physics B - Proceedings Supplements 79, no. 1-3 (1999): 444–46. http://dx.doi.org/10.1016/s0920-5632(99)00748-3.

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47

Caligaris, Marta, Georgina Rodríguez, and Lorena Laugero. "Designing Tools for Numerical Integration." Procedia - Social and Behavioral Sciences 176 (February 2015): 270–75. http://dx.doi.org/10.1016/j.sbspro.2015.01.471.

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48

Rabinowitz, Philip. "Extrapolation methods in numerical integration." Numerical Algorithms 3, no. 1 (1992): 17–28. http://dx.doi.org/10.1007/bf02141912.

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49

Petras, Knut. "Principles of verified numerical integration." Journal of Computational and Applied Mathematics 199, no. 2 (2007): 317–28. http://dx.doi.org/10.1016/j.cam.2005.07.040.

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50

McLachlan, Robert I. "Perspectives on geometric numerical integration." Journal of the Royal Society of New Zealand 49, no. 2 (2019): 114–25. http://dx.doi.org/10.1080/03036758.2018.1564676.

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