Characteristics of Some Inversion Methods of the Integral Laplace Transform

Application of the Laplace integral transform to a wide range of problems leads to a simpler equation for the image of the desired original. The next step is the problem of inversion; i.e., finding the original from its image. Normally, this step cannot be accomplished analytically, leading to the use of approximate inversion methods. This paper examines theoretical error estimates, the rate of convergence of the inversion method and techniques for increasing it, the stability of a method to errors in initial data, the estimation of the conditioning number of systems of linear algebraic equations for finding frameworks and approximate solutions, and the construction and study of delta-shaped kernels representing an approximate solution as a singular integral.