Solution of Integral Equations of the First Kind with Splines and Inversion of the Laplace Transform

This paper discusses the solution of integral equations of the first kind using quadrature formulas and spline approximations. Particular attention is given to the problem of inverting the Laplace transform. The inversion of the Laplace transform is an ill-posed problem. The problem arises when using approximate methods of inversion. Unlike the image, the original may have breakpoints. Of undoubted interest is the task of developing methods for determining possible breakpoints in the original and the magnitude of the jump in the original at these points. This paper discusses the method of finding original jumps. The results of numerical experiments are presented.