On a numerical technique regarding inversion of the Laplace transform

We have discussed a method to convert the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem, and used a regularization method to solve it. We investigated the behavior of the optimal regularization parameter. The optimal choice of parameter in the regularization of ill-posed inverse problems depends on several features of a given problem. We have compared our results with Varahʹs (1979, 1983) results and they are shown in respective diagrams for comparison purposes.