On the properties of some inversion methods of the Laplace transform

The problem of inversion the integral Laplace transform, which belongs to class ill-posed problems, is considered. Integral equations are reduced ill-conditioned systems linear algebraic equations, in unknowns either coefficients series expansion terms special functions, or approximate values desired original at a number points. Described method using quadrature formulas highest degree accuracy and characteristics stability this indicated. Quadrature constructed, adapted for long-term slow processes viscoelasticity. A deformation integration contour Riemann-Mellin formula proposed, leads calculation certain integrals allows obtaining error estimates. described determining possible breakpoints calculating magnitude jump these