Abstract. 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.

Print publication: Issue 2 (April 2006)
Received 28 September 2005, in final form 17 January 2006
Published 22 March 2006