title: Characteristics of convergence and stability of some methods for inverting 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: 2024-05-30T15:34:02Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-05-30T15:34:02Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Lebedeva A.V., Ryabov V.M. Characteristics of convergence and stability of some methods for inverting the Laplace transform. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11 (69), issue 1, pp. 115–130. https://doi.org/10.21638/spbu01.2024.107 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2024.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45454
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. Various inversion methods are considered and their characteristics
  of accuracy and stability are indicated, which must be known when choosing an inversion
  method for solving applied problems. 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.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This paper was prepared with the support by a grant from St. Petersburg 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 11 (69); 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: 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.title
metadata.value: Characteristics of convergence and stability of some methods for inverting the Laplace transform
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 115-130.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45454/1/115-130.pdf
resources.format: Adobe PDF
resources.size: 313,57 kB