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On regularization method for numerical inversion of Laplace transforms

In this paper we consider a new method of constructing regularizing operators of the inverse Laplace transform. The regularizing operators constructed in this work are defined for any image function analytic for Re p > 0. The analytical dependence between exact and regularized solutions allows to analyze the rate of convergence of the regularized solution to the exact one. This analysis is illustrated by graphs and reveals the main features of the numerical inversion of the Laplace transform. The numerical examples illustrating the advantages of the proposed method in stability and accuracy are given.