Regularizing operators of real-valued inverse Laplace Transformation

The article deals with presentation of a regularizing method of inverse Laplace transformation. The method allows us to obtain regularizing operators of inverse Laplace transformation. The considered approach allows us to find a connection between regularized and exact solutions, prove the convergence of the regularized solution to the exact one, and investigate the arising errors analytically. Provided error analysis reflects general features of any method of inversion of real-valued Laplace transforms. Only final step, i.e. evaluation of an integral of the convolution type, requires usage of numerical methods.