On comparison of spline regularization with exponential sampling method for Laplace transform inversion Original Research Article

In this paper we have converted the Laplace transform to an integral equation of the first kind of convolution type, which is an ill-posed problem and used the spline regularization method to solve it. The method is applied to several test examples taken from [J. Math. Comp. 53 (1989) 589; Inverse Problems 10 (1994) 55; J. Sci. Stat. Comp. 4 (1983) 164]. It gives a good approximation to the true solution and compares well with the exponential sampling method given in [Inverse Problems 7 (1991) 1; 7 (1991) 21; 10 (1994) 55]. The results are shown in the table and respective diagrams.