title: On the properties of some inversion methods of the Laplace transform
metadata.name: dc.contributor.author
metadata.value: Lebedeva, Anastasia V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ryabov, Victor M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T19:20:34Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T19:20:34Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lebedeva A. V., Ryabov V.M. On the properties of some inversion methods of the Laplace transform. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 36–46. https://doi.org/10.21638/spbu01.2023.104 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.104
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39324
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of inversion of the integral Laplace transform, which belongs to the class of ill-posed problems, is considered. Integral equations are reduced to ill-conditioned systems of linear algebraic equations, in which the unknowns are either the coefficients of the series expansion in terms of special functions, or the approximate values of the desired original at a number of points. Described method of inversion using special quadrature formulas of the highest degree of accuracy and the characteristics of the accuracy and stability of this method are indicated. Quadrature inversion formulas are constructed, which are adapted for the inversion of long-term and slow processes of linear viscoelasticity. A method of deformation of the integration contour in the Riemann-Mellin inversion formula is proposed, which leads the problem to the calculation of certain integrals and allows obtaining error estimates. A method is described for determining the possible breakpoints of the original and calculating the magnitude of the jump at these points.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This paper was prepared with the support by a grant from StPetersburg State University “Event 3”
  (Pure ID 75207094).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10 (68); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: Laplace transform
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Laplace transform inversion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: system of linear algebraic equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations of the first kind
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quadrature formulas
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ill-posed problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: ill-conditioned problems
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: regularization method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the properties of some inversion methods of the Laplace transform
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15492-Текст статьи-51843-1-2-20230304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39324/1/15492-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51843-1-2-20230304.pdf
resources.format: Adobe PDF
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