A statistical perspective on numerical inversion of Laplace transform

In this paper we have converted the Laplace transform into Fredholm integral equation of the first kind of convolution type, which is an ill-posed problem and used maximum likelihood regularization method to solve it. The method is applied to various test examples taken from the literature. The method gives a good approximation to the true solution and compares well with maximum entropy(23)) and other regularization(32)) methods. Our results confirm that our method is competitive with other recently presented methods. The results are shown in the table and the diagrams.