Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Sevastianov L. A., Lovetskiy K. P., Kulyabov D. S., Sergeev S. V. Numerical solution of first-order exact differential equations by the integrating factor method. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 4, pp. 512-525. DOI: 10.18500/1816-9791-2024-24-4-512-525, EDN: ILSNIX

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2024
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Language: 
English
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.98
DOI: 
10.18500/1816-9791-2024-24-4-512-525
EDN: 
ILSNIX

Numerical solution of first-order exact differential equations by the integrating factor method

Autors: 
Sevastianov Leonid A., Peoples’ Friendship University of Russia named after Patrice Lumumba
Lovetskiy Konstantin P., Peoples’ Friendship University of Russia named after Patrice Lumumba
Kulyabov Dmitry Sergeevich, Peoples’ Friendship University of Russia named after Patrice Lumumba
Sergeev Stepan V., Peoples’ Friendship University of Russia named after Patrice Lumumba
Abstract: 

A numerical algorithm for solving exact differential equations is proposed, based both on the efficient calculation of integrating factors and on a ''new'' numerical method for integrating functions. Robust determination of the integrating factors is implemented by using the Chebyshev interpolation of the desired functions and performing calculations on Gauss – Lobatto grids, which ensure the discrete orthogonality of the Chebyshev matrices. After that, the integration procedure is carried out using the Chebyshev integration matrices. The integrating factor and the final potential of the ODE solution are presented as interpolation polynomials depending on a limited number of numerically recoverable expansion coefficients.

Key words: 
spectral method
collocation
integrating factors
integration matrices
recovery of coefficients
inverse problem
Acknowledgments: 
This work was supported by the RUDN University Scientific Projects Grant System (project No. 021934-0-000, recipient Konstantin P. Lovetskiy) and by the RUDN University Strategic Academic Leadership Program (recipient Dmitry S. Kulyabov, Stepan V. Sergeev). The work of Leonid A. Sevastianov was supported by the Russian Science Foundation (project No. 20-11-20257).
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Received: 
14.09.2023
Accepted: 
04.12.2023
Published: 
29.11.2024
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