This article is cited in 1 paper

MATHEMATICS

Characteristics of convergence and stability of some methods for inverting the Laplace transform

A. V. Lebedeva, V. M. Ryabov

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: 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.

Keywords: Laplace transform, Laplace transform inversion, integral equations of the first kind, quadrature formulas, ill-posed problems, ill-conditioned problems.

UDC: 519.61

MSC: 65F22

Received: 03.02.2023
Revised: 02.05.2023
Accepted: 31.08.2023

DOI: 10.21638/spbu01.2024.107