The work describes the new regularized algorithm for computing integrals of rapidly oscillating functions allowing effectively and accurately determine the required value in the presence of stationary points. In the case where the phase function has stationary points (its derivative vanishes on the interval of integration), the calculation of the corresponding integral is still a sufficiently difficult task even for the Levin method due to the degeneracy of the resulting system of linear equations. The basic idea of regularization, described in the article, is the simultaneous modification of the amplitude and phase functions, which does not change the integrand, but eliminates the degeneracy of the phase function on the interval of integration. The regularized algorithm presented in the work is based on the Levin collocation method and describes the stable method of integration of rapidly oscillating functions at the presence of stationary points. Performance and high accuracy of the algorithms are illustrated by various examples.

Authors

Conference proceedings

Publisher

РУДН

Language

English

Pages

189-196

Status

Published

Link

Volume

2

Year

2016

Organizations

^{1}Peoples Friendship University of Russia

Keywords

regularization; integration of rapidly oscillating functions; Levin collocation method; Chebyshev differentiation matrix; stable methods for solving systems of linear algebraic equations

Date of creation

30.10.2018

Date of change

01.03.2021

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Distributed computer and communication networks: control, computation, communications (DCCN-2016): Proceedings of the Nineteenth International Scientific Conference. Russia, Moscow, 21-25 November 2016. Vol. 2: Mathematical Modeling, Simulation and Control Problems.
РУДН.
Vol. 2.
2016.
P. 159-164

Distributed computer and communication networks: control, computation, communications (DCCN-2016): Proceedings of the Nineteenth International Scientific Conference. Russia, Moscow, 21-25 November 2016. Vol. 2: Mathematical Modeling, Simulation and Control Problems.
РУДН.
Vol. 2.
2016.
P. 204-211