TY - JOUR

T1 - Характеристики сходимости и устойчивости некоторых методов обращения преобразования Лапласа

AU - Лебедева, Анастасия Владимировна

AU - Рябов, Виктор Михайлович

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - https://www.mendeley.com/catalogue/f132846d-5257-33a9-89f8-d4fcf3699038/

U2 - 10.21638/spbu01.2024.107

DO - 10.21638/spbu01.2024.107

M3 - статья

VL - 11(69)

SP - 115

EP - 130

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. МАТЕМАТИКА. МЕХАНИКА. АСТРОНОМИЯ

SN - 1025-3106

IS - 1

ER -