Numerical inversion of the Laplace transform: analysis via regularized analytic continuation

A new stable numerical method for analytic continuation from a line/half-line in the complex plane is proposed and applied to the numerical inversion of the Laplace transform. It is shown that the inversions of real-valued and complex Laplace transforms are two different problems. Several real methods are derived via analytic continuation from the real axis onto the imaginary axis and discussed in detail. The limitations of the most effective real method are considered. An effective criterion for comparing real methods derivable from analytic continuation is proposed and analysed. The effectiveness of this criterion is illustrated using examples.