Numerical solution of first-order exact differential equations by the integrating factor method
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 us...
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| Format: | Article |
| Language: | English |
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Saratov State University
2024-11-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2024/11/512-525-sevastianov_et_al.pdf |
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| _version_ | 1846149891911319552 |
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| author | Sevastianov, Leonid A. Lovetskiy, Konstantin P. Kulyabov, Dmitry Sergeevich Sergeev, Stepan V. |
| author_facet | Sevastianov, Leonid A. Lovetskiy, Konstantin P. Kulyabov, Dmitry Sergeevich Sergeev, Stepan V. |
| author_sort | Sevastianov, Leonid A. |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7d278b76b62a4c19b3178e64e1dcd2dc |
| institution | Kabale University |
| issn | 1816-9791 2541-9005 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj-art-7d278b76b62a4c19b3178e64e1dcd2dc2024-11-29T09:51:53ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052024-11-0124451252510.18500/1816-9791-2024-24-4-512-525Numerical solution of first-order exact differential equations by the integrating factor methodSevastianov, Leonid A.0Lovetskiy, Konstantin P.1Kulyabov, Dmitry Sergeevich2Sergeev, Stepan V.3Peoples’ Friendship University of Russia named after Patrice Lumumba, 6, Miklukho-Maklaya St., Moscow, 117198, RussiaPeoples’ Friendship University of Russia named after Patrice Lumumba, 6, Miklukho-Maklaya St., Moscow, 117198, RussiaPeoples’ Friendship University of Russia named after Patrice Lumumba, 6, Miklukho-Maklaya St., Moscow, 117198, RussiaPeoples’ Friendship University of Russia named after Patrice Lumumba, 6, Miklukho-Maklaya St., Moscow, 117198, RussiaA 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.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2024/11/512-525-sevastianov_et_al.pdfspectral methodcollocationintegrating factorsintegration matricesrecovery of coefficientsinverse problem |
| spellingShingle | Sevastianov, Leonid A. Lovetskiy, Konstantin P. Kulyabov, Dmitry Sergeevich Sergeev, Stepan V. Numerical solution of first-order exact differential equations by the integrating factor method Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика spectral method collocation integrating factors integration matrices recovery of coefficients inverse problem |
| title | Numerical solution of first-order exact differential equations by the integrating factor method |
| title_full | Numerical solution of first-order exact differential equations by the integrating factor method |
| title_fullStr | Numerical solution of first-order exact differential equations by the integrating factor method |
| title_full_unstemmed | Numerical solution of first-order exact differential equations by the integrating factor method |
| title_short | Numerical solution of first-order exact differential equations by the integrating factor method |
| title_sort | numerical solution of first order exact differential equations by the integrating factor method |
| topic | spectral method collocation integrating factors integration matrices recovery of coefficients inverse problem |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2024/11/512-525-sevastianov_et_al.pdf |
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