The Laguerre functions in the inversion of the Laplace transform

Abstract

The authors present a numerical inversion method for the Laplace transform based on the Fourier series of Laguerre functions. They assume that the values of the Laplace transform are given in a finite interval and that they contain noise. The domain of the restored function is (0, infinity ). The convergence of the algorithm is examined and they present a rule for the choice of the Laguerre function parameter. The algorithm is applied to test problems and the results confirm that their algorithm is competitive with others recently presented for this ill-posed problem.