Quadratures with super power convergence

Мұқаба

Дәйексөз келтіру

Толық мәтін

Аннотация

The calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is significantly faster than the power law and is close to exponential one. For integrals with bounded smoothness, power convergence is realized with the maximum achievable order of accuracy.

Авторлар туралы

Aleksandr Belov

M. V. Lomonosov Moscow State University; RUDN University

Хат алмасуға жауапты Автор.
Email: aa.belov@physics.msu.ru
ORCID iD: 0000-0002-0918-9263
Scopus Author ID: 57191950560
ResearcherId: Q-5064-2016

Candidate of Physical and Mathematical Sciences, Researcher of Faculty of Physics, M. V. Lomonosov Moscow State University; Assistant Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia

1, bld. 2, Leninskie Gory, Moscow, 119991, Russian Federation; 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Maxim Tintul

M. V. Lomonosov Moscow State University

Email: maksim.tintul@mail.ru
ORCID iD: 0000-0002-5466-1221

Master’s Degree Student of Faculty of Physics

1, bld. 2, Leninskie Gory, Moscow, 119991, Russian Federation

Valentin Khokhlachev

M. V. Lomonosov Moscow State University

Email: valentin.mycroft@yandex.ru
ORCID iD: 0000-0002-6590-5914

Master’s Degree Student of Faculty of Physics

1, bld. 2, Leninskie Gory, Moscow, 119991, Russian Federation

Әдебиет тізімі

  1. N. N. Kalitkin and E. A. Alshina, Numerical Methods. Vol. 1: Numerical Analysis [Chislennye Metody. T. 1: Chislennyi analiz]. Moscow: Akademiya, 2013, in Russian.
  2. N. N. Kalitkin, A. B. Alshin, E. A. Alshina, and V. B. Rogov, Computations with Quasi-Uniform Grids [Vychisleniya na kvaziravnomernykh setkakh]. Moscow: Fizmatlit, 2005, in Russian.
  3. L. N. Trefethen and J. A. C. Weideman, “The exponentially convergent trapezoidal rule,” SIAM Review, vol. 56, no. 3, pp. 385-458, 2014. doi: 10.1137/130932132.
  4. N. N. Kalitkin and S. A. Kolganov, “Quadrature formulas with exponential convergence and calculation of the Fermi-Dirac integrals,” Doklady Mathematics, vol. 95, no. 2, pp. 157-160, 2017. doi: 10.1134/S1064562417020156.
  5. N. N. Kalitkin and S. A. Kolganov, “Computing the Fermi-Dirac functions by exponentially convergent quadratures,” Mathematical Models and Computer Simulations, vol. 10, no. 4, pp. 472-482, 2018. doi: 10.1134/S2070048218040063.
  6. T. Sag and G. Szekeres, “Numerical evaluation of high-dimensional integrals,” Math. Comp., vol. 18, pp. 245-253, 1964. doi: 10.1090/S0025-5718-1964-0165689-X.
  7. A. Sidi, “Numerical evaluation of high-dimensional integrals,” International Series Numer. Math., vol. 112, pp. 359-373, 1993. doi: 10.1007/978-3-0348-6338-4_27.
  8. M. Iri, S. Moriguti, and Y. Takasawa, “On a certain quadrature formula,” International Series Numer. Math., vol. 17, pp. 3-20, 1987. doi: 10.1016/0377-0427(87)90034-3.
  9. M. Mori, “An IMT-Type Double Exponential Formula for Numerical Integration,” Publ. Res. Inst. Math. Sci. Kyoto Univ., vol. 14, no. 3, pp. 713-729, 1978. doi: 10.2977/prims/1195188835.
  10. A. A. Belov, N. N. Kalitkin, and V. S. Khokhlachev, “Improved error estimates for an exponentially convergent quadratures [Uluchshennyye otsenki pogreshnosti dlya eksponentsial’no skhodyashchikhsya kvadratur],” Preprints of IPM im. M. V. Keldysh, no. 75, 2020, in Russian. doi: 10.20948/prepr-2020-75.
  11. V. S. Khokhlachev, A. A. Belov, and N. N. Kalitkin, “Improvement of error estimates for exponentially convergent quadratures [Uluchsheniye otsenok pogreshnosti dlya eksponentsial’no skhodyashchikhsya kvadratur],” Izv. RAN. Ser. fiz., vol. 85, no. 2, pp. 282-288, 2021, in Russian. doi: 10.31857/S0367676521010166.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу