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THE NUMERICAL INVERSION OF THE LAPLACE TRANSFORM IN REPRODUCING KERNEL HILBERT SPACES
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
Abstract: In this paper we have converted the Laplace transform into an integral equation of the first kind of convolution type, which is an ill-posed problem and used a statistical regularization method to solve it. The method is applied to three examples taken from Rodriguez and Seatzu . It gives a good approximation to the true solution and compares well with the method given by Rodriguez and Seatzu . The results are shown in the Table and the diagrams.
Keywords: Ill-posed problem, inversion of Laplace transform, convolution equation, cross-validation, filter function, regularization parameter.