Determination of breakpoints and the magnitude of the jump of the original according to its Laplace image
DOI:
https://doi.org/10.21638/spbu01.2024.205Abstract
The application of the integral Laplace transform for a wide class of problems leads to a simpler equation for the image of the desired original. At the next step, the inversion problem arises, i. e., finding the original by its image. As a rule, it is not possible to carry out this step analytically. The problem arises of using approximate inversion methods. In this case, the approximate solution is represented as a linear combination of the image and its derivatives at a number of points of the complex half-plane in which the image is regular. However, the original, unlike the image, may even have break points. Of undoubted interest is the task of developing methods for determining the possible break points of the original and the magnitude of the original jump at these points. The proposed methods use the values of high-order image derivatives in order to obtain a satisfactory accuracy of approximate solutions. Methods for accelerating the convergence of the obtained approximations are indicated. The results of numerical experiments illustrating the effectiveness of the proposed methods are presented.Keywords:
Laplace integral transform, inversion problem, original discontinuity points, original jump
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References
Литература
1. Лаврентьев М. А., Шабат Б. В. Методы теории функцийкомплексного переменного. Москва, Лань (2002).
2. Крылов В. И., Скобля Н. С. Методы приближенного преобразования Фурье и обращения преобразования Лапласа. Москва, Наука (1974).
3. Cohen A. M. Numerical methods for Laplace transform inversion. New York, Springer (2007).
4. Рябов В. М. Численное обращение преобразования Лапласа. Санкт-Петербург, Изд-во С.-Петерб. ун-та (2013).
5. Widder D. V. The Laplace transform. Princeton (1946).
6. Натансон И. П. Теория функцийвещественнойпеременной. Москва, Наука (1974).
References
1. Lavrent’ev M. A., Shabat B. V. Methods of the theory of functions of a complex variable. Moscow, Lan’ Publ. (2002). (In Russian)
2. Krylov V. I., Skoblya N. S. Methods of the approximate Fourier transform and the inversion of the Laplace transform. Moscow Publ. (1974). (In Russian)
3. Cohen A. M. Numerical methods for Laplace transform inversion. New York, Springer (2007).
4. Ryabov V. M. Numerical inversion of the Laplace transform. St. Рetersburg, St. Рetersburg University Press (2013). (In Russian)
5. Widder D. V. The Laplace transform. Princeton (1946).
6. Natanson I. P. Theory of functions of a real variable. Moscow, Nauka Publ. (1974). (In Russian)
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Published
2024-08-10
How to Cite
Lebedeva, A. V., & Ryabov, V. M. (2024). Determination of breakpoints and the magnitude of the jump of the original according to its Laplace image. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(2), 316–323. https://doi.org/10.21638/spbu01.2024.205
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
