Quadratures with super power convergence

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Abstract

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.

About the authors

Aleksandr A. Belov

M. V. Lomonosov Moscow State University; RUDN University

Author for correspondence.
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 A. 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 S. 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

References

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